Dissertations / Theses on the topic 'Risk management – Mathematical models'
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1
Basak, Rishi. "Environmental management systems and the intra-firm risk relationship." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0034/MQ64316.pdf.
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Gu, Jiawen, and 古嘉雯. "On credit risk modeling and credit derivatives pricing." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/202367.
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In this thesis, efforts are devoted to the stochastic modeling, measurement and evaluation of credit risks, the development of mathematical and statistical tools to estimate and predict these risks, and methods for solving the significant computational problems arising in this context.
The reduced-form intensity based credit risk models are studied. A new type of reduced-form intensity-based model is introduced, which can incorporate the impacts of both observable trigger events and economic environment on corporate defaults. The key idea of the model is to augment a Cox process with trigger events. In addition, this thesis focuses on the relationship between structural firm value model and reduced-form intensity based model. A continuous time structural asset value model for the asset value of two correlated firms with a two-dimensional Brownian motion is studied. With the incomplete information introduced, the information set available to the market participants includes the default time of each firm and the periodic asset value reports. The original structural model is first transformed into a reduced-form model. Then the conditional distribution of the default time as well as the asset value of each name are derived. The existence of the intensity processes of default times is proven and explicit form of intensity processes is given in this thesis.
Discrete-time Markovian models in credit crisis are considered. Markovian models are proposed to capture the default correlation in a multi-sector economy. The main idea is to describe the infection (defaults) in various sectors by using an epidemic model. Green’s model, an epidemic model, is applied to characterize the infectious effect in each sector and dependence structures among various sectors are also proposed. The models are then applied to the computation of Crisis Value-at-Risk (CVaR) and Crisis Expected Shortfall (CES). The relationship between correlated defaults of different industrial sectors and business cycles as well as the impacts of business cycles on modeling and predicting correlated defaults is investigated using the Probabilistic Boolean Network (PBN). The idea is to model the credit default process by a PBN and the network structure can be inferred by using Markov chain theory and real-world data.
A reduced-form model for economic and recorded default times is proposed and the probability distributions of these two default times are derived. The numerical study on the difference between these two shows that our proposed model can both capture the features and fit the empirical data. A simple and efficient method, based on the ordered default rate, is derived to compute the ordered default time distributions in both the homogeneous case and the two-group heterogeneous case under the interacting intensity default contagion model. Analytical expressions for the ordered default time distributions with recursive formulas for the coefficients are given, which makes the calculation fast and efficient in finding rates of basket CDSs.published_or_final_version
Mathematics
Doctoral
Doctor of Philosophy
3
Liu, Binbin, and 刘彬彬. "Some topics in risk theory and optimal capital allocation problems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B48199291.
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In recent years, the Markov Regime-Switching model and the class of Archimedean
copulas have been widely applied to a variety of finance-related fields. The
Markov Regime-Switching model can reflect the reality that the underlying economy
is changing over time. Archimedean copulas are one of the most popular
classes of copulas because they have closed form expressions and have great flexibility in modeling different kinds of dependencies.
In the thesis, we first consider a discrete-time risk process based on the compound
binomial model with regime-switching. Some general recursive formulas
of the expected penalty function have been obtained. The orderings of ruin probabilities are investigated. In particular, we show that if there exists a stochastic
dominance relationship between random claims at different regimes, then we can
order ruin probabilities under different initial regimes.
Regarding capital allocation problems, which are important areas in finance
and risk management, this thesis studies the problems of optimal allocation of
policy limits and deductibles when the dependence structure among risks is modeled
by an Archimedean copula. By employing the concept of arrangement
increasing and stochastic dominance, useful qualitative results of the optimal
allocations are obtained.
Then we turn our attention to a new family of risk measures satisfying a set
of proposed axioms, which includes the class of distortion risk measures with
concave distortion functions. By minimizing the new risk measures, we consider
the optimal allocation of policy limits and deductibles problems based on the
assumption that for each risk there exists an indicator random variable which
determines whether the risk occurs or not. Several sufficient conditions to order
the optimal allocations are obtained using tools in stochastic dominance theory.published_or_final_version
Statistics and Actuarial Science
Doctoral
Doctor of Philosophy
4
Siu, Kin-bong Bonny, and 蕭健邦. "Expected shortfall and value-at-risk under a model with market risk and credit risk." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37727473.
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Li, Tang, and 李唐. "Markov chain models for re-manufacturing systems and credit risk management." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40203700.
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Terciyanli, Erman. "Alternative Mathematical Models For Revenue Management Problems." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12610711/index.pdf.
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In this study, the seat inventory control problem is considered for airline networks from the
perspective of a risk-averse decision maker. In the revenue management literature, it is generally
assumed that the decision makers are risk-neutral. Therefore, the expected revenue is
maximized without taking the variability or any other risk factor into account. On the other
hand, risk-sensitive approach provides us with more information about the behavior of the
revenue. The risk measure we consider in this study is the probability that revenue is less
than a predetermined threshold level. In the risk-neutral cases, while the expected revenue
is maximized, the probability of revenue being less than such a predetermined level might
be high. We propose three mathematical models to incorporate the risk measure under consideration.
The optimal allocations obtained by these models are numerically evaluated in
simulation studies for example problems. Expected revenue, coefficient of variation, load factor
and probability of the poor performance are the performance measures in the simulation
studies. According to the results of these simulations, it shown that the proposed models can
decrease the variability of the revenue considerably. In other words, the probability of revenue
being less than the threshold level is decreased. Moreover, expected revenue can be increased
in some scenarios by using the proposed models. The approach considered in this thesis is especially proposed for small scale airlines because risk of obtaining revenue less than the
threshold level is more for this type of airlines as compared to large scale airlines.
7
Rong, Yian, and 戎軼安. "Applications of comonotonicity in risk-sharing and optimal allocation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/207205.
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Over the past decades, researchers in economics, financial mathematics and actuarial science have introduced results to the concept of comonotonicity in their respective fields of interest. Comonotonicity is a very strong dependence structure and is very often mistaken as a dependence structure that is too extreme and unrealistic. However, the concept of comonotonicity is actually a useful tool for solving several research and practical problems in capital allocation, risk sharing and optimal allocation.
The first topic of this thesis is focused on the application of comonotonicity in optimal capital allocation. The Enterprise Risk Management process of a financial institution usually contains a procedure to allocate the total risk capital of the company into its different business units. Dhaene et al. (2012) proposed a unifying capital allocation framework by considering some general deviation measures. This general framework is extended to a more general optimization problem of minimizing separable convex function with a linear constraint and box constraints. A new approach of solving this constrained minimization problem explicitly by the concept of comonotonicity is developed. Instead of the traditional Kuhn-Tucker theory, a method of expressing each convex function as the expected stop-loss of some suitable random variable is used to solve the optimization problem. Then, some results in convex analysis with infimum-convolution are derived using the result of this new approach.
Next, Borch's theorem is revisited from the perspective of comonotonicity. The optimal solution to the Pareto optimal risk-sharing problem can be obtained by the Lagrangian method or variational arguments. Here, I propose a new method, which is based on a Breeden-Litzanbeger type integral representation formula for increasing convex functions. It enables the transform of the objective function into a sum of mixtures of stop-losses. Necessary conditions for the existence of optimal solution are then discussed. The explicit solution obtained allows us to show that the risk-sharing problem is indeed a “point-wise” problem, and hence the value function can be obtained immediately using the notion of supremum-convolution in convex analysis.
In addition to the above classical risk-sharing and capital allocation problems, the problem of minimizing a separable convex objective subject to an ordering restriction is then studied. Best et al. (2000) proposed a pool adjacent violators algorithm to compute the optimal solution. Instead, we show that using the concept of comonotonicity and the technique of dynamic programming the solution can be derived in a recursive manner. By identifying the right-hand derivative of the convex functions with distribution functions of some suitable random variables, we rewrite the objective function into a sum of expected deviations. This transformation and the fact that the expected deviation is a convex function enable us to solve the minimizing problem.published_or_final_version
Statistics and Actuarial Science
Doctoral
Doctor of Philosophy
8
Powell, Robert. "Industry value at risk in Australia." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2007. https://ro.ecu.edu.au/theses/297.
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Value at Risk (VaR) models have gained increasing momentum in recent years. Market VaR is an important issue for banks since its adoption as a primary risk metric in the Basel Accords and the requirement that it is calculated on a daily basis. Credit risk modelling has become increasingly important to banks since the advent of Basel 11 which allows banks with sophisticated modelling techniques to use internal models for the purpose of calculating capital requirements. A high level of credit risk is often the key reason behind banks failing or experiencing severe difficulty. Conditional Value at Risk (CVaR) measures extreme risk, and is gaining popularity with the recognition that high losses are often impacted by a small number of extreme events.
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Hao, Fangcheng, and 郝方程. "Options pricing and risk measures under regime-switching models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B4714726X.
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Wei, Zhenghong. "Empirical likelihood based evaluation for value at risk models." HKBU Institutional Repository, 2007. http://repository.hkbu.edu.hk/etd_ra/896.
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蕭德權 and Tak-kuen Siu. "Risk measures in finance and insurance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31242297.
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Kwok, Ho King Calvin Actuarial Studies Australian School of Business UNSW. "Energy price modelling and risk management." Awarded by:University of New South Wales. Actuarial Studies, 2007. http://handle.unsw.edu.au/1959.4/40602.
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This thesis focuses on the development of a forecasting model for short- to medium-term electricity spot prices, based on modelling the dynamics of the supply and demand functions. It is found that the equilibrium assumption frequently adopted in electricity price models does not always hold; to overcome this problem, a notional demand process derived from the market clearing condition is proposed. Not only is this demand process able to capture all the price-affecting factors in one variable, but it also allows the equilibrium assumption to be satisfied and a spot price model to be built, using any appropriate form of hypothetical supply function. In addition, this thesis presents a model for approximating and modelling the bid stacks by capturing the points that govern their shape and location. Integrating these two models provides a realistic model that has a mean absolute percentage error of approximately 19% and 24% for week- and month-ahead forecasts respectively, when applied to the New South Wales (NSW) half-hourly electricity spot prices. Additionally, the density forecasting evaluation method proposed by Diebold et al. (1998) is employed in the thesis to assess the performance of the model. Besides the development of a spot price model, a two-part empirical study is made of the prices of NSW electricity futures contracts. The first part of the study develops a method based on the principle of certainty equivalence, which enables the market utility function to be recovered from a set of futures market quotes. The method is tested with two different sets of simulated data and works as expected. However, it is unable to obtain useful results from the NSW market quotes due to the poor data quality. The second part uses a regression method to investigate the relationship between futures prices and the descriptive statistics of the underlying spot prices. The result suggests that futures prices in NSW are linear combinations of the median and volatility of the final payoff.
13
Li, Yuming. "Univariate and multivariate measures of risk aversion and risk premiums with joint normal distribution and applications in portfolio selection models." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26110.
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This thesis gives the formal derivations of the so-called Rubinstein's measures of risk aversion and their multivariate generalizations. The applications of these measures in portfolio selection models are also presented.
Assuming that a decision maker's preferences can be represented by a unidimensional von Neumann and Morgenstern utility function, we consider a model with an uninsurable initial random wealth and an insurable risk. Under the assumption that the two random variables have a bivariate normal distribution, the second-order co-variance operator is developed from Stein/Rubinstein first-order covariance operator and is used to derive Rubinstein's measures of risk aversion from the approximations of risk premiums. Rubinstein's measures of risk aversion are proved to be the appropriate generalizations of the Arrow-Pratt measures of risk aversion.
In a portfolio selection model with two risky investments having a bivariate normal distribution, we show that Rubinstein's measures of risk aversion can yield the desirable characterizations of risk aversion and wealth effects on the optimal portfolio. These properties of Rubinstein's measures of risk aversion are analogous to those of the Arrow-Pratt measures of risk aversion in the portfolio selection model with one riskless and one risky investment.
In multi-dimensional decision problems, we assume that a decision maker's
preferences can be represented by a multivariate utility function. From the model with an uninsurable initial wealth vector and insurable risk vector having a joint normal distribution in the wealth space, we derived the matrix measures of risk aversion which are the multivariate extension of Rubinstein's measures of risk aversion. The derivations are based on the multivariate version of Stein/Rubinstein covariance operator developed by Gassmann and its second-order generalization to be developed in this thesis.
We finally present an application of the matrix measures of risk aversion in a portfolio selection model with a multivariate utility function and two risky investments.
In this model, if we assume that the random returns on the two investments and other random variables have a joint normal distribution, the optimal portfolio can be characterized by the matrix measures of risk aversion.Business, Sauder School of
Graduate
14
Li, Xiaofei 1972. "Three essays on the pricing of fixed income securities with credit risk." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=84523.
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This thesis studies the impacts of credit risk, or the risk of default, on the pricing of fixed income securities. It consists of three essays. The first essay extends the classical corporate debt pricing model in Merton (1974) to incorporate stochastic volatility (SV) in the underlying firm asset value and derive a closed-form solution for the price of corporate bond. Simulation results show that the SV specification for firm asset value greatly increases the resulting credit spread levels. Therefore, the SV model addresses one major deficiency of the Merton-type models: namely, at short maturities the Merton model is unable to generate credit spreads high enough to be compatible with those observed in the market. In the second essay, we develop a two-factor affine model for the credit spreads on corporate bonds. The first factor can be interpreted as the level of the spread, and the second factor is the volatility of the spread. Our empirical results show that the model is successful at fitting actual corporate bond credit spreads. In addition, key properties of actual credit spreads are better captured by the model. Finally, the third essay proposes a model of interest rate swap spreads. The model accommodates both the default risk inherent in swap contracts and the liquidity difference between the swap and Treasury markets. The default risk and liquidity components of swap spreads are found to behave very differently: first, the default risk component is positively related to the riskless interest rate, whereas the liquidity component is negatively correlated with the riskless interest rate; second, although default risk accounts for the largest share of the levels of swap spreads, the liquidity component is much more volatile; and finally, while the default risk component has been historically positive, the liquidity component was negative for much of the 1990s and has become positive since the financial market turmoil in 1998.
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Liao, Mingwei, and 廖明瑋. "Futures hedging on both procurement risk and sales risk under correlated prices and demand." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/206683.
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The profitability of a manufacturer could be largely affected by underlying uncertainties embedded in the fast-changing business environment. Random factors, such as input material price at the procurement end or output product price and demand at the sales end, might produce significant risks. Effective financial hedging therefore needs to be taken to mitigate these risk exposures. Although it is common to use commodity futures to control the risks at either end separately, little has been done on the hedging of these risk exposures in an integrated manner. Therefore, this study aims to develop a planning approach that performs financial hedging on both the procurement risk and the sales risk in a joint manner.
This planning approach is based on a framework that has a risk-averse commodity processor that procures input commodity and sells output commodity in the spot market, while hedging the procurement risk and sales risk through trading futures contracts in the commodity markets. Both the input and output commodities futures are used for the hedging. A both-end-hedging model is developed to quantitatively evaluate the approach. The evaluation is based on an objective function that considers both profit maximisation and risk mitigation. Decisions on spot procurement, input futures hedging position, and output futures hedging position are optimised simultaneously. As the input commodity is the main production material for the output commodity, positive correlation between the input material price and the output product price is considered. The customer demand is considered negatively correlated with the output product price.
An ethanol plant using corn as the main input material is employed as an example to implement the proposed model. The model is represented as a stochastic program, and the Gibson-Schwartz two-factor model is employed to describe the stochastic commodity prices. Historical commodity price data are used to estimate the parameters for the two-factor model with state-space form and Kalman filter. By generating various scenarios representing evolving prices and the random customer demand, the stochastic program could be solved using linear programming algorithms under its deterministic equivalent.
Numerical experiments are carried out to demonstrate the benefit that could be gained from applying the both-end-hedging approach proposed in this study. Comparing with traditional no-hedging model or single-end-hedging models, the improvement obtained from the proposed model is found to be significant. The effectiveness of the model is further tested in various price trend and price correlation, demand elasticity and volatility, and risk attitude of the decision maker. It is found that the proposed approach is robust in these various circumstances, and the approach is especially effective when the price trend is uncertain and when the decision maker has a strong risk-averse attitude.published_or_final_version
Industrial and Manufacturing Systems Engineering
Master
Master of Philosophy
16
Leboho, Nakedi Wilson. "Quantitative Risk Management and Pricing for Equity Based Insurance Guarantees." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96980.
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Thesis (MSc)--Stellenbosch University, 2015ENGLISH ABSTRACT : Equity-based insurance guarantees also known as unit-linked annuities are annuities with embedded exotic, long-term and path-dependent options which can be categorised into variable and equity indexed annuities, whereby investors participate in the security markets through insurance companies that guarantee them a minimum of their invested premiums. The difference between the financial options and options embedded in equity-based policies is that financial ones are financed by the option buyers’ premiums, whereas options of the equity-based policies are financed by also continuous fees that follow the premium paid first by the policyholders during the life of the contracts. Other important dissimilarities are that equity-based policies do not give the owner the right to sell the contract, and carry not just security market related risk, but also insurance related risks such as the selection rate, behavioural, mortality, others and the systematic longevity. Thus equity-based annuities are much complicated insurance products to precisely value and hedge. For insurance companies to successfully fulfil their promise of eventually returning at least initially invested amount to the policyholders, they have to be able to measure and manage risks within the equity-based policies. So in this thesis, we do fair pricing of the variable and equity indexed annuities, then discuss management of financial market and insurance risks management.
AFRIKAANSE OPSOMMING : Aandeel-gebaseerde versekering waarborg ook bekend as eenheid-gekoppelde annuiteite is eksotiese, langtermyn-en pad-afhanklike opsies wat in veranderlike en gelykheid geindekseer annuiteite, waardeur beleggers neem in die sekuriteit markte deur middel van versekering maatskappye wat waarborg hulle ’n minimum van geklassifiseer kan word hulle belˆe premies. Die verskil tussen die finansi¨ele opsies en opsies is ingesluit in aandele-gebaseerde beleid is dat die finansi¨ele mense is gefinansier deur die opsie kopers se premies, terwyl opsies van die aandele-gebaseerde beleid word deur ook deurlopende fooie wat volg op die premie wat betaal word eers deur die polishouers gefinansier gedurende die lewe van die kontrakte. Ander belangrike verskille is dat aandele-gebaseerde beleid gee nie die eienaar die reg om die kontrak te verkoop, en dra nie net markverwante risiko sekuriteit, maar ook versekering risiko’s, soos die seleksie koers, gedrags, sterftes, ander en die sistematiese langslewendheid. So aandeel-gebaseerde annuiteite baie ingewikkeld versekering produkte om presies waarde en heining. Vir versekeringsmaatskappye suksesvol te vervul hul belofte van uiteindelik ten minste aanvanklik belˆe bedrag terug te keer na die polishouers, hulle moet in staat wees om te meet en te bestuur risiko’s binne die aandeel-gebaseerde beleid. So in hierdie tesis, ons doen billike pryse van die veranderlike en gelykheid geïndekseer annuiteite, bespreek dan die bestuur van finansiele markte en versekering risiko’s bestuur.
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Deng, Hui, and 鄧惠. "Mean-variance optimal portfolio selection with a value-at-risk constraint." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B41897213.
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Xu, Yihua, and 許意華. "Procurement risk management using commodity futures: a multistage stochastic programming approach." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37823413.
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Sagi, Jacob S. "Partial ordering of risky choices : anchoring, preference for flexibility and applications to asset pricing." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0019/NQ56611.pdf.
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Brizendine, Laora Dauberman. "Low probability-high consequence considerations in a multiobjective approach to risk management." Thesis, This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-07112009-040353/.
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Zhu, Dongming 1963. "Asymmetric heavy-tailed distributions : theory and applications to finance and risk management." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=102854.
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This thesis focuses on construction, properties and estimation of asymmetric heavy-tailed distributions, as well as on their applications to financial modeling and risk measurement. First of all, we suggest a general procedure to construct a fully asymmetric distribution based on a symmetrically parametric distribution, and establish some natural relationships between the symmetric and asymmetric distributions. Then, three new classes of asymmetric distributions are proposed by using the procedure: the Asymmetric Exponential Power Distributions (AEPD), the Asymmetric Student-t Distributions (ASTD) and the Asymmetric Generalized t Distribution (AGTD). For the first two distributions, we give an interpretation of their parameters and explore basic properties of them, including moments, expected shortfall, characterization by the maximum entropy property, and the stochastic representation. Although neither distribution satisfies the regularity conditions under which the ML estimators have the usual asymptotics, due to a non-differentiable likelihood function, we nonetheless establish asymptotics for the full MLE of the parameters. A closed-form expression for the Fisher information matrix is derived, and Monte Carlo studies are provided. We also illustrate the usefulness of the GARCH-type models with the AEPD and ASTD innovations in the context of predicting downside market risk of financial assets and demonstrate their superiority over skew-normal and skew-Student's t GARCH models. Finally, two new classes of generalized extreme value distributions, which include Jenkinson's GEV (Generalized Extreme Value) distribution (Jenkinson, 1955) as special cases, are proposed by using the maximum entropy principle, and their properties are investigated in detail.
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Liu, Guochun. "Value at risk models for a nonlinear hedged portfolio." Link to electronic thesis, 2004. http://www.wpi.edu/Pubs/ETD/Available/etd-0430104-155045.
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Rouah, Fabrice. "Essays on hedge funds, operational risk, and commodity trading advisors." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103290.
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Hedge funds report performance information voluntarily. When they stop reporting they are transferred from the "live" pool of funds to the "defunct" pool. Consequently, liquidated funds constitute a subset of the defunct pool. I present models of hedge fund survival, attrition, and survivorship bias based on liquidation alone. This refines estimates of predictor variables in models of survival, leads to attrition rates of hedge funds to be roughly one half those previously thought, and produces larger estimates of survivorship bias. Survival models based on liquidated funds only, lead to an increase in survival time of 50 to 100 percent relative to survival based on all defunct funds.In addition to refining estimates of survival time, it is useful to examine how the double fee structure of hedge funds and Commodity Trading Advisors (CTA) affects the incentives of their managers. Young CTAs are usually very small --- they hold few financial assets --- and may not meet their operating expenses with their management fee alone, so their incentive is to take on risk and post good returns. As they grow, their incentive to take on risk diminishes. CTAs in their fifth year diminish their volatility by 25 percent relative to their first year, and diminish returns by 70 percent. We find CTAs to behave more like indexers as they grow, concerned with more with capital preservation than asset management.
Operational risk is a major cause of hedge fund and CTA liquidation. In the banking industry, regulators have called upon institutions to develop models for measuring capital charge for operational losses, and to subject these models to stress testing. Losses are found to be inversely related to GDP growth, and positively related to unemployment. Since losses are thus cyclical, one way to stress test models is to calculate capital charge during good and bad economic regimes. We find loss distributions to have thicker tails during bad regimes. One implication is that banks will likely need to increase their capital charge when economic conditions deteriorate.
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Ni, Jian, and 倪剑. "Commodity procurement risk management using futures contracts: a dynamic financial hedging approach withmultistage rebalancing." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B46587949.
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Shi, Li, and 时莉. "Long-term commodity procurement risk management using futures contracts: a dynamic stack-and-rollapproach." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B49858749.
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The procurement of commodity materials for production is an important issue in supply chain management. Effective procurement should consider both uncertain customer demand and fluctuating commodity price which, when act together, give rise to the procurement risk. To protect the bottom line, a manufacturer has to plan its procurement activities with special attention given to such procurement risk. Existing research has studied the use of exchange market-traded commodities in mitigating procurement risk. This study addresses the case of a manufacturer with long-term procurement commitments who wishes to hedge against the risk exposure by using long-dated futures contracts. In the commodities markets, however, long-dated futures are often illiquid or even unavailable, thus making the hedge ineffective. Alternatively, in a stack-and-roll hedge, the hedging positions are rolled forward in actively traded short-dated futures contracts of equal maturity until the procurement is executed. This in effect replicates the long-term futures contract in performing a hedge. This study therefore aims at developing a dynamic stack-and-roll approach that can effectively manage the long maturity procurement risk.
The proposed dynamic stack-and-roll approach is inherently a discrete-time hedging strategy that divides the procurement planning horizon into multiple decision stages. The nearby futures are adopted as the short-dated futures as they are typically liquid. The hedging positions are adjusted periodically in response to the commodity price behaviour and updated information about the forward customer demand. For a manufacturer who wishes to mitigate the procurement risk as well as maximise the terminal revenue after the procurement, the mean-variance objective function is employed to model the manufacturer’s risk aversion behaviour. Then, a dynamic program formulation of the approach is presented for determining a closed-form expression of the optimal hedging positions. Notice that the hedging policy is a time-consistent mean-variance policy in discrete-time, in contrast to the existing discrete hedging approaches that employ minimum-variance policies.
In this study, the commodity prices are modelled by a fractal nonlinear regression process that employs a recurrent wavelet neural network as the nonlinear function. The purpose of this arrangement is to incorporate the fractal properties discovered in commodity prices series. In the wavelet transform domain, fractal self-similarity and self-affinity information of the price series over a certain time scale can be extracted. The Extended Kalman Filter (EKF) algorithm is applied to train the neural network for its lower training error comparing with classical gradient descent algorithms. Monthly returns and volatility of commodity prices are estimated by daily returns data in order to increase the estimation accuracy and facilitate effective hedging. The demand information is updated stage by stage using Bayesian inference. The updating process are defined and adapted to a filtration, which can be regarded as the information received at the beginning of each decision stage. Numerical experiments are carried out to evaluate the performance of the proposed stack-and-roll approach. The results show that the proposed approach robustly outperforms other hedging strategies that employ minimum-variance or naïve policies, and effectively mitigate the procurement risk.published_or_final_version
Industrial and Manufacturing Systems Engineering
Doctoral
Doctor of Philosophy
26
Shi, Yuan, and 石园. "A portfolio approach to procurement planning and risk hedging under uncertainty." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44905051.
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Maj, Mateusz. "Essays in risk management: conditional expectation with applications in finance and insurance." Doctoral thesis, Universite Libre de Bruxelles, 2012. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209668.
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In this work we study two problems motivated by Risk Management: the optimal design of financial products from an investor's point of view and the calculation of bounds and approximations for sums involving non-independent random variables. The element that interconnects these two topics is the notion of conditioning, a fundamental concept in probability and statistics which appears to be a useful device in finance. In the first part of the dissertation, we analyse structured products that are now widespread in the banking and insurance industry. These products typically protect the investor against bearish stock markets while offering upside participation when the markets are bullish. Examples of these products include capital guaranteed funds commercialised by banks, and equity linked contracts sold by insurers. The design of these products is complex in general and it is vital to examine to which extent they are actually interesting from the investor's point of view and whether they cannot be dominated by other strategies. In the academic literature on structured products the focus has been almost exclusively on the pricing and hedging of these instruments and less on their performance from an investor's point of view. In this work we analyse the attractiveness of these products. We assess the theoretical cost of inefficiency when buying a structured product and describe the optimal strategy explicitly if possible. Moreover we examine the cost of the inefficiency in practice. We extend the results of Dybvig (1988a, 1988b) and Cox & Leland (1982, 2000) who in the context of a complete, one-dimensional market investigated the inefficiency of path-dependent pay-offs. In the dissertation we consider this problem in one-dimensional Levy and multidimensional Black-Scholes financial markets and we provide evidence that path-dependent pay-offs should not be preferred by decision makers with a fixed investment horizon, and they should buy path-independent structures instead. In these market settings we also demonstrate the optimal contract that provides the given distribution to the consumer, and in the case of risk- averse investors we are able to propose two ways of improving the design of financial products. Finally we illustrate the theory with a few well-known securities and strategies e.g. dollar cost averaging, buy-and-hold investments and widely used portfolio insurance strategies. The second part of the dissertation considers the problem of finding the distribution of a sum of non- independent random variables. Such dependent sums appear quite often in insurance and finance, for instance in case of the aggregate claim distribution or loss distribution of an investment portfolio. An interesting avenue to cope with this problem consists in using so-called convex bounds, studied by Dhaene et al. (2002a, 2002b), who applied these to sums of log-normal random variables. In their papers they have shown how these convex bounds can be used to derive closed-form approximations for several of the risk measures of such a sum. In the dissertation we prove that unlike the log-normal case the construction of a convex lower bound in explicit form appears to be out of reach for general sums of log-elliptical risks and we show how we can construct stop-loss bounds and we use these to construct mean preserving approximations for general sums of log-elliptical distributions in explicit form.Doctorat en Sciences
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Galane, Lesiba Charles. "The risk parity approach to asset allocation." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/95974.
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Thesis (MSc)--Stellenbosch University, 2014.ENGLISH ABSTRACT: We consider the problem of portfolio's asset allocation characterised by risk and return. Prior to the 2007-2008 financial crisis, this important problem was tackled using mainly the Markowitz mean-variance framework. However, throughout the past decade of challenging markets, particularly for equities, this framework has exhibited multiple drawbacks. Today many investors approach this problem with a 'safety first' rule that puts risk management at the heart of decision-making. Risk-based strategies have gained a lot of popularity since the recent financial crisis. One of the 'trendiest' of the modern risk-based strategies is the Risk Parity model, which puts diversification in terms of risk, but not in terms of dollar values, at the core of portfolio risk management. Inspired by the works of Maillard et al. (2010), Bruder and Roncalli (2012), and Roncalli and Weisang (2012), we examine the reliability and relationship between the traditional mean-variance framework and risk parity. We emphasise, through multiple examples, the non-diversification of the traditional mean-variance framework. The central focus of this thesis is on examining the main Risk-Parity strategies, i.e. the Inverse Volatility, Equal Risk Contribution and the Risk Budgeting strategies. Lastly, we turn our attention to the problem of maximizing the absolute expected value of the logarithmic portfolio wealth (sometimes called the drift term) introduced by Oderda (2013). The drift term of the portfolio is given by the sum of the expected price logarithmic growth rate, the expected cash flow, and half of its variance. The solution to this problem is a linear combination of three famous risk-based strategies and the high cash flow return portfolio.
AFRIKAANSE OPSOMMING: Ons kyk na die probleem van batetoewysing in portefeuljes wat gekenmerk word deur risiko en wins. Voor die 2007-2008 finansiele krisis, was hierdie belangrike probleem deur die Markowitz gemiddelde-variansie raamwerk aangepak. Gedurende die afgelope dekade van uitdagende markte, veral vir aandele, het hierdie raamwerk verskeie nadele getoon. Vandag, benader baie beleggers hierdie probleem met 'n 'veiligheid eerste' reël wat risikobestuur in die hart van besluitneming plaas. Risiko-gebaseerde strategieë het baie gewild geword sedert die onlangse finansiële krisis. Een van die gewildste van die moderne risiko-gebaseerde strategieë is die Risiko- Gelykheid model wat diversifikasie in die hart van portefeulje risiko bestuur plaas. Geïnspireer deur die werke van Maillard et al. (2010), Bruder and Roncalli (2012), en Roncalli and Weisang (2012), ondersoek ons die betroubaarheid en verhouding tussen die tradisionele gemiddelde-variansie raamwerk en Risiko- Gelykheid. Ons beklemtoon, deur middel van verskeie voorbeelde, die niediversifikasie van die tradisionele gemiddelde-variansie raamwerk. Die sentrale fokus van hierdie tesis is op die behandeling van Risiko-Gelykheid strategieë, naamlik, die Omgekeerde Volatiliteit, Gelyke Risiko-Bydrae en Risiko Begroting strategieë. Ten slotte, fokus ons aandag op die probleem van maksimering van absolute verwagte waarde van die logaritmiese portefeulje welvaart (soms genoem die drif term) bekendgestel deur Oderda (2013). Die drif term van die portefeulje word gegee deur die som van die verwagte prys logaritmiese groeikoers, die verwagte kontantvloei, en die helfte van die variansie. Die oplossing vir hierdie probleem is 'n lineêre kombinasie van drie bekende risiko-gebaseerde strategieë en die hoë kontantvloei wins portefeulje.
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Kim, Joocheol. "Stochastic programming approach to asset liability management under uncertainty." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/25324.
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Eroglu, Fatma Esra. "Service Models For Airline Revenue Management Problems." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613490/index.pdf.
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In this thesis, the seat inventory control problem is studied for airlines from the perspective
of a risk-averse decision maker. There are only a few studies in the revenue
management literature that consider the risk factor. Most of the studies aim at finding
the optimal seat allocations while maximizing the expected revenue and do not take
the variability of the revenue and hence a risk measure into account. This study aims
to decrease the variance of the revenue by increasing the capacity utilization called
load factor in the revenue management literature. In addition to expected revenue,
load factor is an important performance measure the state companies work with. For
this purpose, two types of models with load factor formulations are proposed. This
thesis is the first study in the revenue management literature for the airline industry
that uses the load factor formulations in the mathematical models. It is an advantage
to work with load factor formulations since the models with load factor formulations
are much easier to formulate and solve as compared to other risk sensitive models in
the literature. The results of the proposed models are evaluated by using simulation
for a sample network under different scenarios. The models we propose allow us to control the variability of revenue by changing the used capacity of the aircraft. This
is at the expense of a decrease in the revenue under some scenarios. The models we
propose perform satisfactorily under all scenarios and they are strongly recommended
to be used especially for the small-scale airline companies and state companies and
for scheduling new flights even in large scale, well established airline companies.
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Shahverdyan, Sergey. "Model free optimisation in risk management." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:6ae9525e-1120-448b-89a2-1670955eb833.
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Following the financial crisis of 2008, the need for more robust techniques to quantify the capital charge for risk management has become a pressing problem. Under Basel II/III, banks are allowed to calculate the capital charge using internally developed models subject to regulatory approval. An interesting problem for the regulator is to compare the resulting figures against the required capital under worst case scenarios. The existing literature on the latter problem, which is based on the marginal problem, assumes that no a-priori information is known about the dependencies of contributing risks. These problems are linear optimisation problems over a constrained set of probability measures, discretisation of which leads to large scale LPs. But this approach is very conservative and cannot be implemented robustly in practice, due to the scarcity of historical data. In our approach, we take a less conservative strategy by incorporating dependence information contained in the data in a form that still leads to LPs, an important feature of such problems due to their high dimensionality. Conceptually, our model is the discretisation of an infinite dimensional linear optimisation problem over a set of probability measures. For some specific cases we can prove strong duality, opening up the approach of discretising the dual instead of the primal. This approach is preferable, as it yields better numerical results. In this work we also apply our model to model-free path-dependent option pricing. Use of delayed column generation techniques allows us to solve problems several orders of magnitude larger than via the standard simplex algorithm. For high-dimensional LPs we also implement Nesterov's smoothing technique to solve the problems.
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Liu, Min, and 劉敏. "Energy allocation with risk management in electricity markets." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B29335978.
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Pang, Long-fung, and 彭朗峯. "Semi-static hedging of guarantees in variable annuities under exponential lévy models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B43572224.
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Yuan, Jiangchuan. "Risk diversification framework in algorithmic trading." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51905.
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We propose a systematic framework for designing adaptive trading strategies that minimize both the mean and the variance of the execution costs. This is achieved by diversifying risk over sequential decisions in discrete time. By incorporating previous trading performance as a state variable, the framework can dynamically adjust the risk-aversion level for future trading. This incorporation also allows the framework to solve the mean-variance problems for different risk aversion factors all at once. After developing this framework, it is then applied to solve three algorithmic trading problems. The first two are trade scheduling problems, which address how to split a large order into sequential small orders in order to best approximate a target price – in our case, either the arrival price, or the Volume-Weighed-Average-Price (VWAP). The third problem is one of optimal execution of the resulting small orders by submitting market and limit orders. Unlike the tradition in both academia and industry of treating the scheduling and order placement problems separately, our approach treats them together and solves them simultaneously. In out-of-sample tests, this unified strategy consistently outperforms strategies that treat the two problems separately.
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Walljee, Raabia. "The Levy-LIBOR model with default risk." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96957.
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Thesis (MSc)--Stellenbosch University, 2015ENGLISH ABSTRACT : In recent years, the use of Lévy processes as a modelling tool has come to be viewed more favourably than the use of the classical Brownian motion setup. The reason for this is that these processes provide more flexibility and also capture more of the ’real world’ dynamics of the model. Hence the use of Lévy processes for financial modelling is a motivating factor behind this research presentation. As a starting point a framework for the LIBOR market model with dynamics driven by a Lévy process instead of the classical Brownian motion setup is presented. When modelling LIBOR rates the use of a more realistic driving process is important since these rates are the most realistic interest rates used in the market of financial trading on a daily basis. Since the financial crisis there has been an increasing demand and need for efficient modelling and management of risk within the market. This has further led to the motivation of the use of Lévy based models for the modelling of credit risky financial instruments. The motivation stems from the basic properties of stationary and independent increments of Lévy processes. With these properties, the model is able to better account for any unexpected behaviour within the market, usually referred to as "jumps". Taking both of these factors into account, there is much motivation for the construction of a model driven by Lévy processes which is able to model credit risk and credit risky instruments. The model for LIBOR rates driven by these processes was first introduced by Eberlein and Özkan (2005) and is known as the Lévy-LIBOR model. In order to account for the credit risk in the market, the Lévy-LIBOR model with default risk was constructed. This was initially done by Kluge (2005) and then formally introduced in the paper by Eberlein et al. (2006). This thesis aims to present the theoretical construction of the model as done in the above mentioned references. The construction includes the consideration of recovery rates associated to the default event as well as a pricing formula for some popular credit derivatives.
AFRIKAANSE OPSOMMING : In onlangse jare, is die gebruik van Lévy-prosesse as ’n modellerings instrument baie meer gunstig gevind as die gebruik van die klassieke Brownse bewegingsproses opstel. Die rede hiervoor is dat hierdie prosesse meer buigsaamheid verskaf en die dinamiek van die model wat die praktyk beskryf, beter hierin vervat word. Dus is die gebruik van Lévy-prosesse vir finansiële modellering ’n motiverende faktor vir hierdie navorsingsaanbieding. As beginput word ’n raamwerk vir die LIBOR mark model met dinamika, gedryf deur ’n Lévy-proses in plaas van die klassieke Brownse bewegings opstel, aangebied. Wanneer LIBOR-koerse gemodelleer word is die gebruik van ’n meer realistiese proses belangriker aangesien hierdie koerse die mees realistiese koerse is wat in die finansiële mark op ’n daaglikse basis gebruik word. Sedert die finansiële krisis was daar ’n toenemende aanvraag en behoefte aan doeltreffende modellering en die bestaan van risiko binne die mark. Dit het verder gelei tot die motivering van Lévy-gebaseerde modelle vir die modellering van finansiële instrumente wat in die besonder aan kridietrisiko onderhewig is. Die motivering spruit uit die basiese eienskappe van stasionêre en onafhanklike inkremente van Lévy-prosesse. Met hierdie eienskappe is die model in staat om enige onverwagte gedrag (bekend as spronge) vas te vang. Deur hierdie faktore in ag te neem, is daar genoeg motivering vir die bou van ’n model gedryf deur Lévy-prosesse wat in staat is om kredietrisiko en instrumente onderhewig hieraan te modelleer. Die model vir LIBOR-koerse gedryf deur hierdie prosesse was oorspronklik bekendgestel deur Eberlein and Özkan (2005) en staan beken as die Lévy-LIBOR model. Om die kredietrisiko in die mark te akkommodeer word die Lévy-LIBOR model met "default risk" gekonstrueer. Dit was aanvanklik deur Kluge (2005) gedoen en formeel in die artikel bekendgestel deur Eberlein et al. (2006). Die doel van hierdie tesis is om die teoretiese konstruksie van die model aan te bied soos gedoen in die bogenoemde verwysings. Die konstruksie sluit ondermeer in die terugkrygingskoers wat met die wanbetaling geassosieer word, sowel as ’n prysingsformule vir ’n paar bekende krediet afgeleide instrumente.
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Wagenaar, Elmien. "A mathematical approach to financial allocation strategies." Thesis, Stellenbosch : Stellenbosch University, 2002. http://hdl.handle.net/10019.1/52648.
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Blatt, Sharon L. "An in-depth look at the information ratio." Link to electronic thesis, 2004. http://www.wpi.edu/Pubs/ETD/Available/etd-0824104-155216/.
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Christoforidou, Amalia. "Regime-switching option pricing models." Thesis, University of Glasgow, 2015. http://theses.gla.ac.uk/6684/.
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Part I: This chapter develops a lattice method for option evaluation aiming to investigate whether the option prices reflect the shifts in the distributions of the underlying asset returns and the risk-free interest rate. More precisely we try to investigate whether the option prices reflect the switches in the correlation between the underlying and risk-free bond returns that characterise different states of the economy. For this reason we develop and test two models. In the first model we allow all the parameters to follow a regime-switching process while in the second model, in order to isolate the regime-switching correlation effect on the option prices, we allow only the correlation to follow a regime-switching process. The models developed use pentanomial lattices to represent the evolution of the regime-switching underlying assets. Our findings suggest that the option prices reflect the regime-switches and that a model which considers these switches could produce more accurate results than a single-regime model. Part II: This part develops a class of closed-form models for options on commodities evaluation under the assumptions of mean-reversion in the commodity prices and factors’ values and regime-switching in the volatilities and correlations. At first we develop novel closed-form solutions of the 1-, 2- and 3-factors models and later in the paper these three models are transformed into regime switching models. The six models (three with and three without regime-switching) are then tested and compared on real market data. Our findings suggest that the by increasing the stochastic factors and assuming regime-switching in the models their flexibility and thus their accuracy increases.
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Li, Xin. "Monte Carlo methods in calculating value at risk." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2148276.
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Hakim, Abdul. "Modelling the interactions across international stock, bond and foreign exchange markets." UWA Business School, 2009. http://theses.library.uwa.edu.au/adt-WU2009.0202.
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[Truncated abstract] Given the theoretical and historical evidence that support the benefit of investing internationally. there is Iittle knowledge available of proper international portfolio construction in terms of how much should be invested in foreign countries, which countries should be targeted, and types of assets to be included in the portfolio. The prospects of these benefits depend on the market volatilities, cross-country correlations, and currency risks to change in the future. Another important issue in international portfolio diversification is the growth of newly emerging markets which have different characteristics from the developed ones. Addressing the issues, the thesis intends to investigate the nature of volatility, conditional correlations, and the impact of currency risks in international portfolio, both in developed and emerging markets. Chapter 2 provides literature review on volatility spillovers, conditional correlations, and forecasting both VaR and conditional correlations using GARCH-type models. Attention is made on the estimated models, type of assets, regions of markets, and tests of forecasts. Chapter 3 investigates the nature of volatility spillovers across intemational assets, which is important in determining the nature of portfolio's volatility when most assets are seems to be connected. ... The impacts of incorporating volatility spillovers and asymmetric effect on the forecast performance of conditional correlation will also be examined in this thesis. The VARMA-AGARCH of McAleer, Hoti and Chan (2008) and the VARMA-GARCH model of Ling and McAleer (2003) will be estimated to accommodate volatility spillovers and asymmetric effect. The CCC model of Bollerslev (1990) will also be estimated as benchmark as the model does not incorporate both volatility spillovers and asymmetric effects. Given the information about the nature of conditional correlations resulted from the forecasts using a rolling window technique, Section 2 of Chapter 4 investigates the nature of conditional correlations by estimating two multivariate GARCH models allowing for time-varying conditional correlations, namely the DCC model of Engle (2002) and the GARCC model of McAleer et al. (2008). Chapter 5 conducts VaR forecast considering the important role of VaR as a standard tool for risk management. Especially, the chapter investigates whether volatility spillovers and time-varying conditional correlations discussed in the previous two chapters are of helps in providing better VaR forecasts. The BEKK model of Engle and Kroner (1995) and the DCC model of Engle (2002) will be estimated to incorporate volatility spillovers and conditional correlations, respectively. The DVEC model of Bollerslev et al. (1998) and the CCC model of Bollerslev (1990) will be estimated to serve benchmarks, as both models do not incorporate both volatility spillovers and timevarying conditional correlations. Chapter 6 concludes the thesis and lists somc possible future research.
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Chun, So Yeon. "Hybrid is good: stochastic optimization and applied statistics for or." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44717.
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In the first part of this thesis, we study revenue management in resource exchange alliances. We first show that without an alliance the sellers will tend to price their products too high and sell too little, thereby foregoing potential profit, especially when capacity is large. This provides an economic motivation for interest in alliances, because the hope may be that some of the foregone profit may be captured under an alliance. We then consider a resource exchange alliance, including the effect of the alliance on competition among
alliance members. We show that the foregone profit may indeed be captured under such an alliance. The problem of determining the optimal amounts of resources to exchange is formulated as a stochastic mathematical program with equilibrium constraints. We demonstrate how to determine whether there exists a unique equilibrium after resource exchange, how to compute the equilibrium, and how to compute the optimal resource exchange.
In the second part of this thesis, we study the estimation of risk measures in risk management. In the financial industry, sell-side analysts periodically publish recommendations of underlying securities with target prices. However, this type of analysis does not provide risk measures associated with underlying companies. In this study, we discuss linear regression approaches to the estimation of law invariant conditional risk measures. Two estimation procedures are considered and compared; one is based on residual analysis of
the standard least squares method and the other is in the spirit of the M-estimation approach used in robust statistics. In particular, Value-at-Risk and Average Value-at-Risk measures are discussed in detail. Large sample statistical inference of the estimators is derived. Furthermore, finite sample properties of the proposed estimators are investigated and compared with theoretical derivations in an extensive Monte Carlo study. Empirical results on the real data (different financial asset classes) are also provided to illustrate the performance of the estimators.
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Babenko, V. A. "Dynamical models of the minimax program management of innovation processes in interprises with risks." Thesis, NTU "KhPI", 2016. http://repository.kpi.kharkov.ua/handle/KhPI-Press/26209.
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Dicks, Anelda. "Value at risk and expected shortfall : traditional measures and extreme value theory enhancements with a South African market application." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85674.
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Thesis (MComm)--Stellenbosch University, 2013.ENGLISH ABSTRACT: Accurate estimation of Value at Risk (VaR) and Expected Shortfall (ES) is critical in the management of extreme market risks. These risks occur with small probability, but the financial impacts could be large. Traditional models to estimate VaR and ES are investigated. Following usual practice, 99% 10 day VaR and ES measures are calculated. A comprehensive theoretical background is first provided and then the models are applied to the Africa Financials Index from 29/01/1996 to 30/04/2013. The models considered include independent, identically distributed (i.i.d.) models and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) stochastic volatility models. Extreme Value Theory (EVT) models that focus especially on extreme market returns are also investigated. For this, the Peaks Over Threshold (POT) approach to EVT is followed. For the calculation of VaR, various scaling methods from one day to ten days are considered and their performance evaluated. The GARCH models fail to converge during periods of extreme returns. During these periods, EVT forecast results may be used. As a novel approach, this study considers the augmentation of the GARCH models with EVT forecasts. The two-step procedure of pre-filtering with a GARCH model and then applying EVT, as suggested by McNeil (1999), is also investigated. This study identifies some of the practical issues in model fitting. It is shown that no single forecasting model is universally optimal and the choice will depend on the nature of the data. For this data series, the best approach was to augment the GARCH stochastic volatility models with EVT forecasts during periods where the first do not converge. Model performance is judged by the actual number of VaR and ES violations compared to the expected number. The expected number is taken as the number of return observations over the entire sample period, multiplied by 0.01 for 99% VaR and ES calculations.
AFRIKAANSE OPSOMMING: Akkurate beraming van Waarde op Risiko (Value at Risk) en Verwagte Tekort (Expected Shortfall) is krities vir die bestuur van ekstreme mark risiko’s. Hierdie risiko’s kom met klein waarskynlikheid voor, maar die finansiële impakte is potensieel groot. Tradisionele modelle om Waarde op Risiko en Verwagte Tekort te beraam, word ondersoek. In ooreenstemming met die algemene praktyk, word 99% 10 dag maatstawwe bereken. ‘n Omvattende teoretiese agtergrond word eers gegee en daarna word die modelle toegepas op die Africa Financials Index vanaf 29/01/1996 tot 30/04/2013. Die modelle wat oorweeg word sluit onafhanklike, identies verdeelde modelle en Veralgemeende Auto-regressiewe Voorwaardelike Heteroskedastiese (GARCH) stogastiese volatiliteitsmodelle in. Ekstreemwaarde Teorie modelle, wat spesifiek op ekstreme mark opbrengste fokus, word ook ondersoek. In hierdie verband word die Peaks Over Threshold (POT) benadering tot Ekstreemwaarde Teorie gevolg. Vir die berekening van Waarde op Risiko word verskillende skaleringsmetodes van een dag na tien dae oorweeg en die prestasie van elk word ge-evalueer. Die GARCH modelle konvergeer nie gedurende tydperke van ekstreme opbrengste nie. Gedurende hierdie tydperke, kan Ekstreemwaarde Teorie modelle gebruik word. As ‘n nuwe benadering oorweeg hierdie studie die aanvulling van die GARCH modelle met Ekstreemwaarde Teorie vooruitskattings. Die sogenaamde twee-stap prosedure wat voor-af filtrering met ‘n GARCH model behels, gevolg deur die toepassing van Ekstreemwaarde Teorie (soos voorgestel deur McNeil, 1999), word ook ondersoek. Hierdie studie identifiseer sommige van die praktiese probleme in model passing. Daar word gewys dat geen enkele vooruistkattingsmodel universeel optimaal is nie en die keuse van die model hang af van die aard van die data. Die beste benadering vir die data reeks wat in hierdie studie gebruik word, was om die GARCH stogastiese volatiliteitsmodelle met Ekstreemwaarde Teorie vooruitskattings aan te vul waar die voorafgenoemde nie konvergeer nie. Die prestasie van die modelle word beoordeel deur die werklike aantal Waarde op Risiko en Verwagte Tekort oortredings met die verwagte aantal te vergelyk. Die verwagte aantal word geneem as die aantal obrengste waargeneem oor die hele steekproefperiode, vermenigvuldig met 0.01 vir die 99% Waarde op Risiko en Verwagte Tekort berekeninge.
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Rahantamialisoa, Tahirivonizaka Fanirisoa Zazaravaka. "Interest rates market and models after the 2007 credit crunch." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/20413.
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Thesis (MSc)--Stellenbosch University, 2012.ENGLISH ABSTRACT: The interest rates market has changed dramatically since the 2007 credit crunch with the explosion of basis spreads between rates of different tenors and currencies. Consequently, the classical replication of FRA rates with spot LIBOR rates is no longer valid. Moreover, the 2007 credit crunch yields a separation between the curve used for discounting and the forward or projection curves that estimate all future cash-fl ows. Another impact of the credit crunch in risk management is that market participants have started to give more importance to the difference between collateralized and uncollateralized trades. Nowadays, the wide spread use of collateral, especially in swap contracts, has made the overnight index swap (OIS) rate the appropriate benchmark for discounting collateralized trades. Inspired by the seminal works of Mercurio (2010a,b), Kijima et al. (2008), Fujii et al. (2011), Bianchetti (2010b), with the contributions of other authors, and motivated by the evolution of the interest rates market and models, this thesis examines a new framework that uses multiple-curves to value interest rate derivatives which is compatible with the current market practice. Firstly, we discuss the roots of the 2007 credit crunch and its serious consequences for pricing interest rate derivatives. We underscore the necessity of a multiple-curve pricing framework for interest rate derivatives. This is followed by a discussion on the importance of collateralization and OIS discounting in pricing Over-The-Counter (OTC) derivatives. The central part of the thesis discusses the modern theoretical framework and the practical implementation of the multiple curve pricing method. We present a bootstrapping algorithm used to construct and fit the multiple-yield curves to market prices of plainvanilla contracts. Secondly, starting with the single-currency economy, the extended version of the LIBOR Market Model, developed by Mercurio (2010a,b), which proposes a joint model of FRA rates, implied forward rates and their corresponding spread is investigated. Analogously, the extended version of short-rate model in a multiple-curve setup and in the presence of basis spread, proposed by Kijima et al. (2008), is presented and discussed. This work provides a detailed analysis of these extensions and the corresponding closed formulae for liquid products such as caps and swaptions. Finally, in the multiple-currencies case, the HJM model with stochastic basis spreads, introduced by Fujii et al. (2011), consistent with the foreign exchange and cross-currency swaps markets that includes the effect of collateralization is examined thoroughly.
AFRIKAANSE OPSOMMING: Die rentekoers mark het dramaties verander sedert die 2007 krediet krisis met 'n ontplo ng van basisverspreidings tussen koerse van verskillende looptye ("tenor") en geldeenhede. As gevolg, is die klassieke replikasie van FRA koerse met LIBOR sigkoerse nie langer geldig nie. Verder het die 2007 kredietkrisis 'n skeiding veroorsaak tussen die kromme wat gebruik word vir diskontering en die voorwaardse of vooruitskattings krommes wat toekomstige kontantvloei voorspel. 'n Verdere impak van die kredietkrisis in risikobestuur is dat mark deelnemers begin het om meer klem te lê op verskille tussen aangevulde en onaangevulde handel. Deesdae, met die algemene gebruik van kollaterale sekuriteit, veral in ruiltransaksiekontrakte, is die oornagse indeks ruiltransaksie (overnight index swap, OIS) koers die geskikte maatstaf om aangevulde handel te diskonteer. Geïnspireer deur die gedagteryke werk van Mercurio (2010a,b), Kijima et al. (2008), Fujii et al. (2011), Bianchetti (2010b), met bydrae van menige outeurs, en gemotiveer deur die evolusie van die rentekoers markte en modelle, ondersoek hierdie tesis 'n nuwe raamwerk wat multikrommes gebruik om rentekoers afgeleide effekte te waardeer wat versoenbaar is met die lopende mark praktyk. Eerstens, bespreek ons die oorsake van die 2007 kredietkrisis en die ernstige nagevolge vir die waardering van rentekoers afgeleide effekte. Ons beklemtoon die noodsaaklikheid van 'n multikromme waarderings raamwerk vir rentekoers afgeleide effekte. Dit word gevolg deur 'n bespreking oor die belangrikheid van aanvulling en OIS diskontering in die waardering van oor-die-toonbank (over-the-counter, OTC) effekte. Die teoretiese raamwerk en die praktiese implimentering van die multikromme waarderings metode word bespreek. Ons stel ook ten toon 'n skoenlus ("bootstrapping") algoritme wat gebruik kan word om meervoudige opbrengs krommes saam te stel en die dan te pas op mark pryse van vanielje kontrakte. Tweedens, met 'n enkel geldeenheid ekonomie as beginpunt, word die uitgebreide weergawe van die LIBOR Mark Model (ontwikkel deur Mercurio (2010a,b), wat 'n gesamentlike model van FRA koerse voorstel), geïmpliseerde termyn koerse en hul ooreenstemmende verspreiding bestudeer. Ooreenkomstig word die uitgebreide weergawe van die kort koers model in 'n multikromme opset en in die aanwesigheid van basisspreiding (voorgestel deur Kijima et al. (2008)) uiteengesit en bespreek. Hierdie werk verskaf 'n uitvoerige analise van hierdie uitbreidings en die ooreenstemmende geslote formules vir vloeibare produkte soos perke en ruiltransaksie opsies. Ten slotte, in die multi-geldeenheid geval, word die HJM model met stogastiese basisverspreiding (voorgestel deur Fujii et al. (2011)), nie-strydig met buitelandse valuta en kruisvaluta ruiltransaksie markte wat die effekte van aanvulling insluit word deuglik bestudeer.
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Castro, Carlos. "Essays in dependence and optimality in large portfolios." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210186.
Full textAbstract:
This thesis is composed of three chapters. The first two chapters provides novel approaches formodeling and estimating the dependence structure for a large portfolio of assets using rating data.
In both chapters a natural form of organizing a portfolio in terms of the levels of exposure to economic sectors and geographical regions, plays a key role in setting up the dependence structure.
The last chapter investigates weather financial strategies that exploit sector or geographical heterogeneity in the asset space are relevant in terms of portfolio optimization. This is also done in a context of a large portfolio but with data on stock returns.
Doctorat en Sciences économiques et de gestion
info:eu-repo/semantics/nonPublished
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"The term structure of credit risk." Thesis, 2000. http://library.cuhk.edu.hk/record=b6073914.
Full textAbstract:
Credit risk is an important source of risk for almost all of the financial securities. The frequent and serious financial crisis has made credit risk a sensitive and crucial consideration for financial institutions, corporations, and individual investors. The accurate pricing for credit risk and credit risky assets depends crucially upon the credit risk term structure---it implies the market expectation for the future credit risk. However, the credit risk analysis is still in its very early stages of development. The investigation about the credit risk term structure, especially the empirical exploration, has many blank points. Earlier research on the credit risk term structure mainly concentrates on the slopes, pertaining to the simple linear term structure which is not applicable to the middle credit quality assets. Thus the curvature of the spread curves may infer snore information about the changes of future credit qualities, the credit cycles, and the recurring business cycles. In this thesis, a bond pair approach is developed to study the shape (curvature as well as slope) of individual spread curves, and the relationship among spread curves for bonds with different ratings. We uncover downward sloping spread curves for triple C and double C bonds and upward sloping spread curves for triple A+ and triple A bonds. We also uncover hump-shaped spread curves for middle-graded bonds including double A to single B, and there exist peak points on these spread curves. We document the relationship among spread curves for bonds with different ratings In terms of time to peak and peak spread. We conclude that, in comparing higher rated bonds (say, double A) with lower rated bonds (say, single B), the credit spread is higher and time to peak is shorter for the latter than the former. In particular, these hump-shaped curves are bounded from above by downward sloping spread curves for triple C and double C bonds and bounded from below by upward sloping spread curves for triple A+ and triple A bonds. These findings provide a good explanation for the middle-rated bonds' spread curves. This evidence helps us to better understand the credit risk term structure, to accurately price credit risk and credit risky assets, and to appropriately manage credit risk.Hu Wen-wei.
"August 2000."
Adviser: Jia He.
Source: Dissertation Abstracts International, Volume: 61-08, Section: A, page: 3284.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2000.
Includes bibliographical references (p. 93-111).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts in English and Chinese.
School code: 1307.
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"Multi-period cooperative investment game with risk." 2008. http://library.cuhk.edu.hk/record=b5893772.
Full textAbstract:
Zhou, Ying.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.
Includes bibliographical references (leaves 89-91).
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Background --- p.1
Chapter 1.2 --- Aims and objectives --- p.2
Chapter 1.3 --- Outline of the thesis --- p.3
Chapter 2 --- Literature Review --- p.6
Chapter 2.1 --- Portfolio Optimization Problems --- p.6
Chapter 2.2 --- Cooperative Games and Cooperative Investment Models --- p.8
Chapter 2.2.1 --- Linear Production Games And Basic Concepts of Co- operative Game Theory --- p.9
Chapter 2.2.2 --- Investment Models Using Linear Production Games --- p.12
Chapter 3 --- Multi-period Cooperative Investment Games: Basic Model --- p.15
Chapter 3.1 --- Cooperative Investment Game under Deterministic Case --- p.16
Chapter 3.2 --- Cooperative Investment Game with Stochastic Return --- p.18
Chapter 3.2.1 --- Basic Assumptions --- p.18
Chapter 3.2.2 --- Choose the Proper Risk Measure --- p.20
Chapter 3.2.3 --- One Period Case --- p.21
Chapter 3.2.4 --- Multi-Period Case --- p.23
Chapter 4 --- The Two-Period Investment Game under L∞ Risk Measure --- p.26
Chapter 4.1 --- The Two Period Model --- p.26
Chapter 4.2 --- The Algorithm --- p.35
Chapter 4.3 --- Optimal Solution of the Dual --- p.41
Chapter 5 --- Primal Solution and Stability of the Core under Two-Period Case --- p.43
Chapter 5.1 --- Direct Results --- p.44
Chapter 5.2 --- Find the Optimal Solutions of the Primal Problem --- p.46
Chapter 5.3 --- Relationship between A and the Core --- p.53
Chapter 5.3.1 --- Tracing out the efficient frontier --- p.54
Chapter 6 --- Multi-Period Case --- p.63
Chapter 6.1 --- Common Risk Price and the Negotiation Process with Concave Risk Utility --- p.64
Chapter 6.1.1 --- Existence of Common Risk Price and Core --- p.65
Chapter 6.1.2 --- Negotiation Process --- p.68
Chapter 6.2 --- Modified Simplex Method --- p.71
Chapter 7 --- Other Risk Measures --- p.76
Chapter 7.1 --- The Downside Risk Measure --- p.76
Chapter 7.1.1 --- Discrete (Finite Scenario) Distributions --- p.78
Chapter 7.1.2 --- General Distributions --- p.81
Chapter 7.2 --- Coherent Risk Measure and CVaR --- p.83
Chapter 8 --- Conclusion and Future Work --- p.87
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"Modeling financial risk: from uni- to bi-directional." 2005. http://library.cuhk.edu.hk/record=b5892708.
Full textAbstract:
Yeung Kin Bong.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.
Includes bibliographical references (leaves 69-73).
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Credit risk modeling --- p.3
Chapter 1.2 --- Uniqueness of bi-directional: hybrid system --- p.4
Chapter 1.3 --- Scope of the study --- p.5
Chapter 2 --- Literature Review --- p.6
Chapter 2.1 --- Statistical / Empirical approach --- p.6
Chapter 2.2 --- Structural approach --- p.8
Chapter 3 --- Background --- p.10
Chapter 3.1 --- Merton structural default model --- p.10
Chapter 3.2 --- Cross-sectional regression analysis (CRA) --- p.15
Chapter 3.3 --- Neural network learning (NN) --- p.16
Chapter 3.3.1 --- Single-layer network --- p.17
Chapter 3.3.2 --- Multi-layer perceptron (MLP) --- p.20
Chapter 3.3.3 --- Back-propagation network --- p.22
Chapter 3.3.4 --- "Supervised, unsupervised and combine unsupervised-supervised learning" --- p.23
Chapter 3.4 --- Weaknesses of uni-directional modeling --- p.23
Chapter 4 --- Methodology --- p.26
Chapter 4.1 --- Bi-directional modeling --- p.26
Chapter 4.2 --- Asset price estimation --- p.31
Chapter 4.3 --- Quantifying accounting data noise --- p.33
Chapter 5 --- Proposed Model --- p.37
Chapter 5.1 --- Core of the model --- p.37
Chapter 5.2 --- Feature selection --- p.41
Chapter 5.3 --- Bi-directional default neural system --- p.44
Chapter 6 --- Implementations --- p.49
Chapter 6.1 --- Data preparation --- p.50
Chapter 6.2 --- Experiment --- p.51
Chapter 6.3 --- Empirical results --- p.61
Chapter 6.3.1 --- Predicted spreads from the uni-directional models --- p.61
Chapter 6.3.2 --- Predicted spreads from the proposed bi-directional model --- p.63
Chapter 6.3.3 --- Performance comparison --- p.64
Chapter 7 --- Conclusions --- p.67
Bibliography --- p.69
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"Portfolio selection under downside risk measure and distributional uncertainties." 2004. http://library.cuhk.edu.hk/record=b5892126.
Full textAbstract:
Chen Li.Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.
Includes bibliographical references (leaves 76-78).
Abstracts in English and Chinese.
Abstract --- p.i
Acknowledgements --- p.iii
Table of Contents --- p.v
Chapter 1 --- Introduction --- p.1
Chapter 2 --- Literature review --- p.4
Chapter 3 --- The semi-mean target tracking model --- p.9
Chapter 3.1 --- Introduction --- p.9
Chapter 3.2 --- The robust optimization problem --- p.11
Chapter 3.3 --- Portfolio selection methods --- p.14
Chapter 3.3.1 --- Jensen's inequality approach --- p.15
Chapter 3.3.2 --- The robust optimization approach --- p.17
Chapter 3.3.3 --- Empirical method --- p.22
Chapter 3.4 --- How to evaluate a portfolio? --- p.24
Chapter 3.4.1 --- Tight bounds --- p.24
Chapter 3.4.2 --- The semidefinite programming bounds --- p.25
Chapter 3.4.3 --- Conclusions --- p.28
Chapter 3.5 --- Numerical results --- p.29
Chapter 3.5.1 --- The analysis of the data --- p.29
Chapter 3.5.2 --- Jensen's inequality approach --- p.31
Chapter 3.5.3 --- The robust optimization approach --- p.34
Chapter 3.5.4 --- The empirical linear programming method --- p.34
Chapter 3.6 --- Comparisons and conclusions --- p.39
Chapter 4 --- The semi-variance target tracking model --- p.45
Chapter 4.1 --- Introduction --- p.45
Chapter 4.2 --- The portfolio selection methods --- p.46
Chapter 4.2.1 --- The robust optimization method --- p.47
Chapter 4.2.2 --- The empirical method --- p.50
Chapter 4.3 --- Evaluating a selected portfolio --- p.52
Chapter 4.3.1 --- Computing SDP bounds --- p.52
Chapter 4.3.2 --- Conclusions --- p.55
Chapter 4.4 --- Numerical results --- p.55
Chapter 4.4.1 --- The robust optimization method --- p.56
Chapter 4.4.2 --- The empirical second order cone programming method --- p.61
Chapter 4.4.3 --- Comparisons and conclusions --- p.61
Chapter 4.5 --- Summary and future work --- p.69
Appendix A --- p.70
Bibliography --- p.76
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Khatywa, Thembalethu. "Mathematical models of credit management and credit derivatives." Thesis, 2010. http://hdl.handle.net/11394/3529.
Full textAbstract:
>Magister Scientiae - MScThe first two chapters give the background, history and overview of the dissertation, together with the necessary mathematical preliminaries. Thereafter, the next four chapters deal with credit risk and credit derivatives.The final part of the dissertation is devoted to the Basel II bank regulatory framework and the mathematical modeling of asset allocation in bank management, pertaining to credit risk.Credit risk models can be categorized into two groups known as structural models and reduced form models. These models are used in pricing and hedging credit risk. In this thesis we review a variety of credit risk instruments described by models of the said types. One of the strategies utilized by companies to mitigate credit risk is by using credit derivatives.In this thesis, five main types of risk derivatives have been considered: credit swaps, credit linked notes, credit spreads, total return swaps and collaterized debt obligations. Valuation models for the first three derivatives that are mentioned above, are also presented in this dissertation.The material presented include some of the most recent developments in the literature. Our methods range from single-period modeling to application of stochastic optimal control theory. We expand on the material presented from the literature by way of simplifying or clarifying proofs, and by adding illustrative examples in the form of calculations, tables and simulations.Also, the entire Chapter 6 is a new original contribution to the existing literature on mathematical modeling of credit risk. Key words: credit risk; default risk; structural approach; reduced form approach; incomplete information approach; investment strategy; Basel II regulatory framework