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Mimouni, Karim. "Three essays on volatility specification in option valuation." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103274.
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Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. However, relatively little is known about the empirical shortcomings of this model. In the first essay, we investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources. We first use realized volatilities to assess the properties of the SQR model and to guide us in the search for alternative specifications. We then estimate the models using maximum likelihood on a long sample of S& P500 returns. Finally, we employ nonlinear least squares on a time series of cross sections of option data. In the estimations on returns and options data, we use the particle filtering technique to retrieve the spot volatility path. The three sources of data we employ all point to the same conclusion: the SQR model is misspecified. Overall, the best of alternative volatility specifications is a model we refer to as the VAR model, which is of the GARCH diffusion type.In the second essay, we estimate the Constant Elasticity of Variance (CEV) model in order to study the level of nonlinearity in the volatility dynamic. We also estimate a CEV process combined with a jump process (CEVJ) and analyze the effects of the jump component on the nonlinearity coefficient. Estimation is performed using the particle filtering technique on a long series of S&P500 returns and on options data. We find that both returns data and returns-and-options data favor nonlinear specifications for the volatility dynamic, suggesting that the extensive use of linear models is not supported empirically. We also find that the inclusion of jumps does not affect the level of nonlinearity and does not improve the CEV model fit.
The third essay provides an empirical comparison of two classes of option valuation models: continuous-time models and discrete-time models. The literature provides some theoretical limit results for these types of dynamics, and researchers have used these limit results to argue that the performance of certain discrete-time and continuous-time models ought to be very similar. This interpretation is somewhat contentious, because a given discrete-time model can have several continuous-time limits, and a given continuous-time model can be the limit for more than one discrete-time model. Therefore, it is imperative to investigate whether there exist similarities between these specifications from an empirical perspective. Using data on S&P500 returns and call options, we find that the discrete-time models investigated in this paper have the same performance in fitting the data as selected continuous-time models both in and out-of-sample.
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Dharmawan, Komang School of Mathematics UNSW. "Superreplication method for multi-asset barrier options." Awarded by:University of New South Wales. School of Mathematics, 2005. http://handle.unsw.edu.au/1959.4/30169.
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The aim of this thesis is to study multi-asset barrier options, where the volatilities of the stocks are assumed to define a matrix-valued bounded stochastic process. The bounds on volatilities may represent, for instance, the extreme values of the volatilities of traded options. As the volatilities are not known exactly, the value of the option can not be determined. Nevertheless, it is possible to calculate extreme values. We show that these values correspond to the best and the worst case scenarios of the future volatilities for short positions and long positions in the portfolio of the options. Our main tool is the equivalence of the option pricing and a certain stochastic control problem and the resulting concept of superhedging. This concept has been well known for some time but never applied to barrier options. First, we prove the dynamic programming principle (DPP) for the control problem. Next, using rather standard arguments we derive the Hamilton-Jacobi-Bellman equation for the value function. We show that the value function is a unique viscosity solution of the Hamilton-Jacobi-Bellman equation. Then we define the super price and superhedging strategy for the barrier options and show equivalence with the control problem studied above. The superprice price can be found by solving the nonlinear Hamilton-Jacobi-Equation studied above. It is called sometimes the Black-Scholes-Barenblatt (BSB) equation. This is the Hamilton-Jacobi-Bellman equation of the exit control problem. The sup term in the BSB equation is determined dynamically: it is either the upper bound or the lower bound of the volatility matrix, according to the convexity or concavity of the value function with respect to the stock prices. By utilizing a probabilistic approach, we show that the value function of the exit control problem is continuous. Then, we also obtain bounds for the first derivative of the value function with respect to the space variable. This derivative has an important financial interpretation. Namely, it allows us to define the superhedging strategy. We include an example: pricing and hedging of a single-asset barrier option and its numerical solution using the finite difference method.
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Wang, Yintian 1976. "Three essays on volatility long memory and European option valuation." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=102851.
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This dissertation is in the form of three essays on the topic of component and long memory GARCH models. The unifying feature of the thesis is the focus on investigating European index option evaluation using these models.The first essay presents a new model for the valuation of European options. In this model, the volatility of returns consists of two components. One of these components is a long-run component that can be modeled as fully persistent. The other component is short-run and has zero mean. The model can be viewed as an affine version of Engle and Lee (1999), allowing for easy valuation of European options. The model substantially outperforms a benchmark single-component volatility model that is well established in the literature. It also fits options better than a model that combines conditional heteroskedasticity and Poisson normal jumps. While the improvement in the component model's performance is partly due to its improved ability to capture the structure of the smirk and the path of spot volatility, its most distinctive feature is its ability to model the term structure. This feature enables the component model to jointly model long-maturity and short-maturity options.
The second essay derives two new GARCH variance component models with non-normal innovations. One of these models has an affine structure and leads to a closed-form option valuation formula. The other model has a non-affine structure and hence, option valuation is carried out using Monte Carlo simulation. We provide an empirical comparison of these two new component models and the respective special cases with normal innovations. We also compare the four component models against GARCH(1,1) models which they nest. All eight models are estimated using MLE on S&P500 returns. The likelihood criterion strongly favors the component models as well as non-normal innovations. The properties of the non-affine models differ significantly from those of the affine models. Evaluating the performance of component variance specifications for option valuation using parameter estimates from returns data also provides strong support for component models. However, support for non-normal innovations and non-affine structure is less convincing for option valuation.
The third essay aims to investigate the impact of long memory in volatility on European option valuation. We mainly compare two groups of GARCH models that allow for long memory in volatility. They are the component Heston-Nandi GARCH model developed in the first essay, in which the volatility of returns consists of a long-run and a short-run component, and a fractionally integrated Heston-Nandi GARCH (FIHNGARCH) model based on Bollerslev and Mikkelsen (1999). We investigate the performance of the models using S&P500 index returns and cross-sections of European options data. The component GARCH model slightly outperforms the FIGARCH in fitting return data but significantly dominates the FIHNGARCH in capturing option prices. The findings are mainly due to the shorter memory of the FIHNGARCH model, which may be attributed to an artificially prolonged leverage effect that results from fractional integration and the limitations of the affine structure.
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Endekovski, Jessica. "Pricing multi-asset options in exponential levy models." Master's thesis, Faculty of Commerce, 2019. http://hdl.handle.net/11427/31437.
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This dissertation looks at implementing exponential Levy models whereby the un- ´ derlyings are driven by Levy processes, which are able to account for stylised facts ´ that traditional models do not, in order to price basket options more efficiently. In particular, two exponential Levy models are implemented and tested: the multi- ´ variate Variance Gamma (VG) model and the multivariate normal inverse Gaussian (NIG) model. Both models are calibrated to real market data and then used to price basket options, where the underlyings are the constituents of the KBW Bank Index. Two pricing methods are also compared: a closed-form (analytical) approximation of the price, derived by Linders and Stassen (2016) and the standard Monte Carlo method. The convergence of the analytical approximation to Monte Carlo prices was found to improve as the time to maturity of the option increased. In comparison to real market data, the multivariate NIG model was able to fit the data more accurately for shorter maturities and the multivariate VG model for longer maturities. However, when looking at Monte Carlo prices, the multivariate VG model was found to outperform the results of the multivariate NIG model, as it was able to converge to Monte Carlo prices to a greater degree.
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Glover, Elistan Nicholas. "Analytic pricing of American put options." Thesis, Rhodes University, 2009. http://hdl.handle.net/10962/d1002804.
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American options are the most commonly traded financial derivatives in the market. Pricing these options fairly, so as to avoid arbitrage, is of paramount importance. Closed form solutions for American put options cannot be utilised in practice and so numerical techniques are employed. This thesis looks at the work done by other researchers to find an analytic solution to the American put option pricing problem and suggests a practical method, that uses Monte Carlo simulation, to approximate the American put option price. The theory behind option pricing is first discussed using a discrete model. Once the concepts of arbitrage-free pricing and hedging have been dealt with, this model is extended to a continuous-time setting. Martingale theory is introduced to put the option pricing theory in a more formal framework. The construction of a hedging portfolio is discussed in detail and it is shown how financial derivatives are priced according to a unique riskneutral probability measure. Black-Scholes model is discussed and utilised to find closed form solutions to European style options. American options are discussed in detail and it is shown that under certain conditions, American style options can be solved according to closed form solutions. Various numerical techniques are presented to approximate the true American put option price. Chief among these methods is the Richardson extrapolation on a sequence of Bermudan options method that was developed by Geske and Johnson. This model is extended to a Repeated-Richardson extrapolation technique. Finally, a Monte Carlo simulation is used to approximate Bermudan put options. These values are then extrapolated to approximate the price of an American put option. The use of extrapolation techniques was hampered by the presence of non-uniform convergence of the Bermudan put option sequence. When convergence was uniform, the approximations were accurate up to a few cents difference.
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Song, Na, and 宋娜. "Mathematical models and numerical algorithms for option pricing and optimal trading." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50662168.
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Research conducted in mathematical finance focuses on the quantitative modeling of financial markets. It allows one to solve financial problems by using mathematical methods and provides understanding and prediction of the complicated financial behaviors. In this thesis, efforts are devoted to derive and extend stochastic optimization models in financial economics and establish practical algorithms for representing and solving problems in mathematical finance.
An option gives the holder the right, but not the obligation, to buy or sell an underlying asset at a specified strike price on or before a specified date. In this thesis, a valuation model for a perpetual convertible bond is developed when the price dynamics of the underlying share are governed by Markovian regime-switching models. By making use of the relationship between the convertible bond and an American option, the valuation of a perpetual convertible bond can be transformed into an optimal stopping problem. A novel approach is also proposed to discuss an optimal inventory level of a retail product from a real option perspective in this thesis. The expected present value of the net profit from selling the product which is the objective function of the optimal inventory problem can be given by the actuarial value of a real option. Hence, option pricing techniques are adopted to solve the optimal inventory problem in this thesis.
The goal of risk management is to eliminate or minimize the level of risk associated with a business operation. In the risk measurement literature, there is relatively little amount of work focusing on the risk measurement and management of interest rate instruments. This thesis concerns about building a risk measurement framework based on some modern risk measures, such as Value-at-Risk (VaR) and Expected Shortfall (ES), for describing and quantifying the risk of interest rate sensitive instruments. From the lessons of the recent financial turmoils, it is understood that maximizing profits is not the only objective that needs to be taken into account. The consideration for risk control is of primal importance. Hence, an optimal submission problem of bid and ask quotes in the presence of risk constraints is studied in this thesis. The optimal submission problem of bid and ask quotes is formulated as a stochastic optimal control problem.
Portfolio management is a professional management of various securities and assets in order to match investment objectives and balance risk against performance. Different choices of time series models for asset price may lead to different portfolio management strategies. In this thesis, a discrete-time dynamic programming approach which is flexible enough to deal with the optimal asset allocation problem under a general stochastic dynamical system is explored. It’s also interesting to analyze the implications of the heteroscedastic effect described by a continuous-time stochastic volatility model for evaluating risk of a cash management problem. In this thesis, a continuous-time dynamic programming approach is employed to investigate the cash management problem under stochastic volatility model and constant volatility model respectively.published_or_final_version
Mathematics
Doctoral
Doctor of Philosophy
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Lee, Mou Chin. "An empirical test of variance gamma options pricing model on Hang Seng index options." HKBU Institutional Repository, 2000. http://repository.hkbu.edu.hk/etd_ra/263.
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Zhao, Jing Ya. "Numerical methods for pricing Bermudan barrier options." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2592939.
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Cisneros-Molina, Myriam. "Mathematical methods for valuation and risk assessment of investment projects and real options." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491350.
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In this thesis, we study the problems of risk measurement, valuation and hedging of financial positions in incomplete markets when an insufficient number of assets are available for investment (real options). We work closely with three measures of risk: Worst-Case Scenario (WCS) (the supremum of expected values over a set of given probability measures), Value-at-Risk (VaR) and Average Value-at-Risk (AVaR), and analyse the problem of hedging derivative securities depending on a non-traded asset, defined in terms of the risk measures via their acceptance sets. The hedging problem associated to VaR is the problem of minimising the expected shortfall. For WCS, the hedging problem turns out to be a robust version of minimising the expected shortfall; and as AVaR can be seen as a particular case of WCS, its hedging problem is also related to the minimisation of expected shortfall. Under some sufficient conditions, we solve explicitly the minimal expected shortfall problem in a discrete-time setting of two assets driven by correlated binomial models. In the continuous-time case, we analyse the problem of measuring risk by WCS, VaR and AVaR on positions modelled as Markov diffusion processes and develop some results on transformations of Markov processes to apply to the risk measurement of derivative securities. In all cases, we characterise the risk of a position as the solution of a partial differential equation of second order with boundary conditions. In relation to the valuation and hedging of derivative securities, and in the search for explicit solutions, we analyse a variant of the robust version of the expected shortfall hedging problem. Instead of taking the loss function $l(x) = [x]^+$ we work with the strictly increasing, strictly convex function $L_{\epsilon}(x) = \epsilon \log \left( \frac{1+exp\{−x/\epsilon\} }{ exp\{−x/\epsilon\} } \right)$. Clearly $lim_{\epsilon \rightarrow 0} L_{\epsilon}(x) = l(x)$. The reformulation to the problem for L_{\epsilon}(x) also allow us to use directly the dual theory under robust preferences recently developed in [82]. Due to the fact that the function $L_{\epsilon}(x)$ is not separable in its variables, we are not able to solve explicitly, but instead, we use a power series approximation in the dual variables. It turns out that the approximated solution corresponds to the robust version of a utility maximisation problem with exponential preferences $(U(x) = −\frac{1}{\gamma}e^{-\gamma x})$ for a preferenes parameter $\gamma = 1/\epsilon$. For the approximated problem, we analyse the cases with and without random endowment, and obtain an expression for the utility indifference bid price of a derivative security which depends only on the non-traded asset.
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Welihockyj, Alexander. "The cost of using misspecified models to exercise and hedge American options on coupon bearing bonds." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/20532.
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This dissertation investigates the cost of using single-factor models to exercise and hedge American options on South African coupon bearing bonds, when the simulated market term structure is driven by a two-factor model. Even if the single factor models are re-calibrated on a daily basis to the term structure, we find that the exercise and hedge strategies can be suboptimal and incur large losses. There is a vast body of research suggesting that real market term structures are in actual fact driven by multiple factors, so suboptimal losses can be largely reduced by simply employing a well-specified multi-factor model.
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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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Montsho, Obakeng Johannes. "Real options valuation for South African nuclear waste management using a fuzzy mathematical approach." Thesis, Rhodes University, 2013. http://hdl.handle.net/10962/d1003051.
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The feasibility of capital projects in an uncertain world can be determined in several ways. One of these methods is real options valuation which arose from financial option valuation theory. On the other hand fuzzy set theory was developed as a mathematical framework to capture uncertainty in project management. The valuation of real options using fuzzy numbers represents an important refinement to determining capital projects' feasibility using the real options approach. The aim of this study is to determine whether the deferral of the decommissioning time (by a decade) of an electricity-generating nuclear plant in South Africa increases decommissioning costs. Using the fuzzy binomial approach, decommissioning costs increase when decommissioning is postponed by a decade whereas use of the fuzzy Black-Scholes approach yields the opposite result. A python code was developed to assist in the computation of fuzzy binomial trees required in our study and the results of the program are incorporated in this thesis.KMBT_363
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Nhongo, Tawuya D. R. "Pricing exotic options using C++." Thesis, Rhodes University, 2007. http://hdl.handle.net/10962/d1008373.
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This document demonstrates the use of the C++ programming language as a simulation tool in the efficient pricing of exotic European options. Extensions to the basic problem of simulation pricing are undertaken including variance reduction by conditional expectation, control and antithetic variates. Ultimately we were able to produce a modularized, easily extend-able program which effectively makes use of Monte Carlo simulation techniques to price lookback, Asian and barrier exotic options. Theories of variance reduction were validated except in cases where we used control variates in combination with the other variance reduction techniques in which case we observed increased variance. Again, the main aim of this half thesis was to produce a C++ program which would produce stable pricings of exotic options.
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劉伯文 and Pak-man Lau. "Option pricing: a survey." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B31977911.
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Chan, Ka Hou. "European call option pricing under partial information." Thesis, University of Macau, 2017. http://umaclib3.umac.mo/record=b3691380.
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Le, Truc. "Stochastic volatility models." Monash University, School of Mathematical Sciences, 2005. http://arrow.monash.edu.au/hdl/1959.1/5181.
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Weng, Zuo Qiu. "Pricing discretely monitored barrier options via a fast and accurate FFT-based method." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2148272.
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Li, Chao. "Option pricing with generalized continuous time random walk models." Thesis, Queen Mary, University of London, 2016. http://qmro.qmul.ac.uk/xmlui/handle/123456789/23202.
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The pricing of options is one of the key problems in mathematical finance. In recent years, pricing models that are based on the continuous time random walk (CTRW), an anomalous diffusive random walk model widely used in physics, have been introduced. In this thesis, we investigate the pricing of European call options with CTRW and generalized CTRW models within the Black-Scholes framework. Here, the non-Markovian character of the underlying pricing model is manifest in Black-Scholes PDEs with fractional time derivatives containing memory terms. The inclusion of non-zero interest rates leads to a distinction between different types of \forward" and \backward" options, which are easily mapped onto each other in the standard Markovian framework, but exhibit significant dfferences in the non-Markovian case. The backward-type options require us in particular to include the multi-point statistics of the non-Markovian pricing model. Using a representation of the CTRW in terms of a subordination (time change) of a normal diffusive process with an inverse L evy-stable process, analytical results can be obtained. The extension of the formalism to arbitrary waiting time distributions and general payoff functions is discussed. The pricing of path-dependent Asian options leads to further distinctions between different variants of the subordination. We obtain analytical results that relate the option price to the solution of generalized Feynman-Kac equations containing non-local time derivatives such as the fractional substantial derivative. Results for L evy-stable and tempered L evy-stable subordinators, power options, arithmetic and geometric Asian options are presented.
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Cheng, Xin. "Three essays on volatility forecasting." HKBU Institutional Repository, 2010. http://repository.hkbu.edu.hk/etd_ra/1183.
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Au, Chi Yan. "Numerical methods for solving Markov chain driven Black-Scholes model." HKBU Institutional Repository, 2010. http://repository.hkbu.edu.hk/etd_ra/1154.
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Chu, Kut-leung, and 朱吉樑. "The CEV model: estimation and optionpricing." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B4257500X.
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Yiu, Fan-lai, and 姚勳禮. "Applicability of various option pricing models in Hong Kong warrants market." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B3126590X.
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Liu, Xin. "Fast exponential time integration scheme and extrapolation method for pricing option with jump diffusions." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2148264.
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高志強 and Chi-keung Anthony Ko. "A preliminary study of Hong Kong warrants using the Black-Scholesoption pricing model." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1985. http://hub.hku.hk/bib/B31263227.
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Lee, Tsz Ho. "High order compact scheme and its applications in computational finance." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2148266.
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Chavanasporn, Walailuck. "Application of stochastic differential equations and real option theory in investment decision problems." Thesis, University of St Andrews, 2010. http://hdl.handle.net/10023/1691.
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This thesis contains a discussion of four problems arising from the application of stochastic differential equations and real option theory to investment decision problems in a continuous-time framework. It is based on four papers written jointly with the author’s supervisor. In the first problem, we study an evolutionary stock market model in a continuous-time framework where uncertainty in dividends is produced by a single Wiener process. The model is an adaptation to a continuous-time framework of a discrete evolutionary stock market model developed by Evstigneev, Hens and Schenk-Hoppé (2006). We consider the case of fix-mix strategies and derive the stochastic differential equations which determine the evolution of the wealth processes of the various market players. The wealth dynamics for various initial set-ups of the market are simulated. In the second problem, we apply an entry-exit model in real option theory to study concessionary agreements between a private company and a state government to run a privatised business or project. The private company can choose the time to enter into the agreement and can also choose the time to exit the agreement if the project becomes unprofitable. An early termination of the agreement by the company might mean that it has to pay a penalty fee to the government. Optimal times for the company to enter and exit the agreement are calculated. The dynamics of the project are assumed to follow either a geometric mean reversion process or geometric Brownian motion. A comparative analysis is provided. Particular emphasis is given to the role of uncertainty and how uncertainty affects the average time that the concessionary agreement is active. The effect of uncertainty is studied by using Monte Carlo simulation. In the third problem, we study numerical methods for solving stochastic optimal control problems which are linear in the control. In particular, we investigate methods based on spline functions for solving the two-point boundary value problems that arise from the method of dynamic programming. In the general case, where only the value function and its first derivative are guaranteed to be continuous, piecewise quadratic polynomials are used in the solution. However, under certain conditions, the continuity of the second derivative is also guaranteed. In this case, piecewise cubic polynomials are used in the solution. We show how the computational time and memory requirements of the solution algorithm can be improved by effectively reducing the dimension of the problem. Numerical examples which demonstrate the effectiveness of our method are provided. Lastly, we study the situation where, by partial privatisation, a government gives a private company the opportunity to invest in a government-owned business. After payment of an initial instalment cost, the private company’s investments are assumed to be flexible within a range [0, k] while the investment in the business continues. We model the problem in a real option framework and use a geometric mean reversion process to describe the dynamics of the business. We use the method of dynamic programming to determine the optimal time for the private company to enter and pay the initial instalment cost as well as the optimal dynamic investment strategy that it follows afterwards. Since an analytic solution cannot be obtained for the dynamic programming equations, we use quadratic splines to obtain a numerical solution. Finally we determine the optimal degree of privatisation in our model from the perspective of the government.
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West, Lydia. "American Monte Carlo option pricing under pure jump levy models." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/79994.
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Thesis (MSc)--Stellenbosch University, 2013.ENGLISH ABSTRACT: We study Monte Carlo methods for pricing American options where the stock price dynamics follow exponential pure jump L évy models. Only stock price dynamics for a single underlying are considered. The thesis begins with a general introduction to American Monte Carlo methods. We then consider two classes of these methods. The fi rst class involves regression - we briefly consider the regression method of Tsitsiklis and Van Roy [2001] and analyse in detail the least squares Monte Carlo method of Longsta and Schwartz [2001]. The variance reduction techniques of Rasmussen [2005] applicable to the least squares Monte Carlo method, are also considered. The stochastic mesh method of Broadie and Glasserman [2004] falls into the second class we study. Furthermore, we consider the dual method, independently studied by Andersen and Broadie [2004], Rogers [2002] and Haugh and Kogan [March 2004] which generates a high bias estimate from a stopping rule. The rules we consider are estimates of the boundary between the continuation and exercise regions of the option. We analyse in detail how to obtain such an estimate in the least squares Monte Carlo and stochastic mesh methods. These models are implemented using both a pseudo-random number generator, and the preferred choice of a quasi-random number generator with bridge sampling. As a base case, these methods are implemented where the stock price process follows geometric Brownian motion. However the focus of the thesis is to implement the Monte Carlo methods for two pure jump L évy models, namely the variance gamma and the normal inverse Gaussian models. We first provide a broad discussion on some of the properties of L évy processes, followed by a study of the variance gamma model of Madan et al. [1998] and the normal inverse Gaussian model of Barndor -Nielsen [1995]. We also provide an implementation of a variation of the calibration procedure of Cont and Tankov [2004b] for these models. We conclude with an analysis of results obtained from pricing American options using these models.
AFRIKAANSE OPSOMMING: Ons bestudeer Monte Carlo metodes wat Amerikaanse opsies, waar die aandeleprys dinamika die patroon van die eksponensiële suiwer sprong L évy modelle volg, prys. Ons neem slegs aandeleprys dinamika vir 'n enkele aandeel in ag. Die tesis begin met 'n algemene inleiding tot Amerikaanse Monte Carlo metodes. Daarna bestudeer ons twee klasse metodes. Die eerste behels regressie - ons bestudeer die regressiemetode van Tsitsiklis and Van Roy [2001] vlugtig en analiseer die least squares Monte Carlo metode van Longsta and Schwartz [2001] in detail. Ons gee ook aandag aan die variansie reduksie tegnieke van Rasmussen [2005] wat van toepassing is op die least squares Monte Carlo metodes. Die stochastic mesh metode van Broadie and Glasserman [2004] val in die tweede klas wat ons onder oë neem. Ons sal ook aandag gee aan die dual metode, wat 'n hoë bias skatting van 'n stop reël skep, en afsonderlik deur Andersen and Broadie [2004], Rogers [2002] and Haugh and Kogan [March 2004] bestudeer is. Die reëls wat ons bestudeer is skattings van die grense tussen die voortsettings- en oefenareas van die opsie. Ons analiseer in detail hoe om so 'n benadering in die least squares Monte Carlo en stochastic mesh metodes te verkry. Hierdie modelle word geï mplementeer deur beide die pseudo kansgetalgenerator en die verkose beste quasi kansgetalgenerator met brug steekproefneming te gebruik. As 'n basisgeval word hierdie metodes geï mplimenteer wanneer die aandeleprysproses 'n geometriese Browniese beweging volg. Die fokus van die tesis is om die Monte Carlo metodes vir twee suiwer sprong L évy modelle, naamlik die variance gamma en die normal inverse Gaussian modelle, te implimenteer. Eers bespreek ons in breë trekke sommige van die eienskappe van L évy prossesse en vervolgens bestudeer ons die variance gamma model soos in Madan et al. [1998] en die normal inverse Gaussian model soos in Barndor -Nielsen [1995]. Ons gee ook 'n implimentering van 'n variasie van die kalibreringsprosedure deur Cont and Tankov [2004b] vir hierdie modelle. Ons sluit af met die resultate wat verkry is, deur Amerikaanse opsies met behulp van hierdie modelle te prys.
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Huang, Ning Ying. "Numerical methods for early-exercise option pricing via Fourier analysis." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2148270.
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Lam, Yue-kwong, and 林宇光. "A revisit to the applicability of option pricing models on the Hong Kong warrants market after the stock option is introduced." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1996. http://hub.hku.hk/bib/B31267282.
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U, Sio Chong. "The applications of Fourier analysis to European option pricing." Thesis, University of Macau, 2009. http://umaclib3.umac.mo/record=b2148263.
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Mboussa, Anga Gael. "Calibration and Model Risk in the Pricing of Exotic Options Under Pure-Jump Lévy Dynamics." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/98030.
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Thesis (MSc)--Stellenbosch University, 2015AFRIKAANSE OPSOMMING : Die groeiende belangstelling in kalibrering en modelrisiko is ’n redelik resente ontwikkeling in finansiële wiskunde. Hierdie proefskrif fokusseer op hierdie sake, veral in verband met die prysbepaling van vanielje-en eksotiese opsies, en vergelyk die prestasie van verskeie Lévy modelle. ’n Nuwe metode om modelrisiko te meet word ook voorgestel (hoofstuk 6). Ons kalibreer eers verskeie Lévy modelle aan die log-opbrengs van die S&P500 indeks. Statistiese toetse en grafieke voorstellings toon albei aan dat suiwer sprongmodelle (VG, NIG en CGMY) die verdeling van die opbrengs beter beskryf as die Black-Scholes model. Daarna kalibreer ons hierdie vier modelle aan S&P500 indeks opsie data en ook aan "CGMY-wˆ ereld" data (’n gesimuleerde wÃłreld wat beskryf word deur die CGMY-model) met behulp van die wortel van gemiddelde kwadraat fout. Die CGMY model vaar beter as die VG, NIG en Black-Scholes modelle. Ons waarneem ook ’n effense verskil tussen die nuwe parameters van CGMY model en sy wisselende parameters, ten spyte van die feit dat CGMY model gekalibreer is aan die "CGMYwêreld" data. Versperrings-en terugblik opsies word daarna geprys, deur gebruik te maak van die gekalibreerde parameters vir ons modelle. Hierdie pryse word dan vergelyk met die "ware" pryse (bereken met die ware parameters van die "CGMY-wêreld), en ’n beduidende verskil tussen die modelpryse en die "ware" pryse word waargeneem. Ons eindig met ’n poging om hierdie modelrisiko te kwantiseer
ENGLISH ABSTRACT : The growing interest in calibration and model risk is a fairly recent development in financial mathematics. This thesis focussing on these issues, particularly in relation to the pricing of vanilla and exotic options, and compare the performance of various Lévy models. A new method to measure model risk is also proposed (Chapter 6). We calibrate only several Lévy models to the log-return of S&P500 index data. Statistical tests and graphs representations both show that pure jump models (VG, NIG and CGMY) the distribution of the proceeds better described as the Black-Scholes model. Then we calibrate these four models to the S&P500 index option data and also to "CGMY-world" data (a simulated world described by the CGMY model) using the root mean square error. Which CGMY model outperform VG, NIG and Black-Scholes models. We observe also a slight difference between the new parameters of CGMY model and its varying parameters, despite the fact that CGMY model is calibrated to the "CGMY-world" data. Barriers and lookback options are then priced, making use of the calibrated parameters for our models. These prices are then compared with the "real" prices (calculated with the true parameters of the "CGMY world), and a significant difference between the model prices and the "real" rates are observed. We end with an attempt to quantization this model risk.
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Lee, Chi-ming Simon, and 李志明. "A study of Hong Kong foreign exchange warrants pricing using black-scholes formula." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1992. http://hub.hku.hk/bib/B3126542X.
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Lee, Jinpyo. "A method for distribution network design and models for option-contracting strategy with buyers' learning." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/29620.
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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.Committee Chair: Kleywegt, Anton J.; Committee Member: Ayhan, Hayriye; Committee Member: Dai, Jim; Committee Member: Erera, Alan; Committee Member: Ward, Amy R. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Rich, Don R. "Incorporating default risk into the Black-Scholes model using stochastic barrier option pricing theory." Diss., This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-06062008-171359/.
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Ng, Man Yun. "Quasi-Monte Carlo methods and their applications in high dimensional option pricing." Thesis, University of Macau, 2011. http://umaclib3.umac.mo/record=b2493256.
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Diallo, Ibrahima. "Some topics in mathematical finance: Asian basket option pricing, Optimal investment strategies." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210165.
Full textAbstract:
This thesis presents the main results of my research in the field of computational finance and portfolios optimization. We focus on pricing Asian basket options and portfolio problems in the presence of inflation with stochastic interest rates.In Chapter 2, we concentrate upon the derivation of bounds for European-style discrete arithmetic Asian basket options in a Black and Scholes framework.We start from methods used for basket options and Asian options. First, we use the general approach for deriving upper and lower bounds for stop-loss premia of sums of non-independent random variables as in Kaas et al. [Upper and lower bounds for sums of random variables, Insurance Math. Econom. 27 (2000) 151–168] or Dhaene et al. [The concept of comonotonicity in actuarial science and finance: theory, Insurance Math. Econom. 31(1) (2002) 3–33]. We generalize the methods in Deelstra et al. [Pricing of arithmetic basket options by conditioning, Insurance Math. Econom. 34 (2004) 55–57] and Vanmaele et al. [Bounds for the price of discrete sampled arithmetic Asian options, J. Comput. Appl. Math. 185(1) (2006) 51–90]. Afterwards we show how to derive an analytical closed-form expression for a lower bound in the non-comonotonic case. Finally, we derive upper bounds for Asian basket options by applying techniques as in Thompson [Fast narrow bounds on the value of Asian options, Working Paper, University of Cambridge, 1999] and Lord [Partially exact and bounded approximations for arithmetic Asian options, J. Comput. Finance 10 (2) (2006) 1–52]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and time-to-maturity
In Chapter 3, we propose some moment matching pricing methods for European-style discrete arithmetic Asian basket options in a Black & Scholes framework. We generalize the approach of Curran M. (1994) [Valuing Asian and portfolio by conditioning on the geometric mean price”, Management science, 40, 1705-1711] and of Deelstra G. Liinev J. and Vanmaele M. (2004) [Pricing of arithmetic basket options by conditioning”, Insurance: Mathematics & Economics] in several ways. We create a framework that allows for a whole class of conditioning random variables which are normally distributed. We moment match not only with a lognormal random variable but also with a log-extended-skew-normal random variable. We also improve the bounds of Deelstra G. Diallo I. and Vanmaele M. (2008). [Bounds for Asian basket options”, Journal of Computational and Applied Mathematics, 218, 215-228]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and
time-to-maturity.
In Chapter 4, we use the stochastic dynamic programming approach in order to extend
Brennan and Xia’s unconstrained optimal portfolio strategies by investigating the case in which interest rates and inflation rates follow affine dynamics which combine the model of Cox et al. (1985) [A Theory of the Term Structure of Interest Rates, Econometrica, 53(2), 385-408] and the model of Vasicek (1977) [An equilibrium characterization of the term structure, Journal of Financial Economics, 5, 177-188]. We first derive the nominal price of a zero coupon bond by using the evolution PDE which can be solved by reducing the problem to the solution of three ordinary differential equations (ODE). To solve the corresponding control problems we apply a verification theorem without the usual Lipschitz assumption given in Korn R. and Kraft H.(2001)[A Stochastic control approach to portfolio problems with stochastic interest rates, SIAM Journal on Control and Optimization, 40(4), 1250-1269] or Kraft(2004)[Optimal Portfolio with Stochastic Interest Rates and Defaultable Assets, Springer, Berlin].
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Cozma, Andrei. "Numerical methods for foreign exchange option pricing under hybrid stochastic and local volatility models." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:44a27fbc-1b7a-4f1a-bd2d-abeb38bf1ff7.
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In this thesis, we study the FX option pricing problem and put forward a 4-factor hybrid stochastic-local volatility model. The model, which describes the dynamics of an exchange rate, its volatility and the domestic and foreign short rates, allows for a perfect calibration to European options and has a good hedging performance. Due to the high-dimensionality of the problem, we propose a Monte Carlo simulation scheme that combines the full truncation Euler scheme for the stochastic volatility component and the stochastic short rates with the log-Euler scheme for the exchange rate. We analyze exponential integrability properties of Euler discretizations for the square-root process driving the stochastic volatility and the short rates, properties which play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a large class of stochastic differential equations in finance, including the ones studied in this thesis. Hence, we prove the strong convergence of the exchange rate approximations and the convergence of Monte Carlo estimators for a number of vanilla and exotic options. Then, we calibrate the model to market data and discuss its fitness for pricing FX options. Next, due to the relatively slow convergence of the Monte Carlo method in the number of simulations, we examine a variance reduction technique obtained by mixing Monte Carlo and finite difference methods via conditioning. We consider a purely stochastic version of the model and price vanilla and exotic options by simulating the paths of the volatility and the short rates, and then evaluating the "inner" Black-Scholes-type expectation by means of a partial differential equation. We prove the convergence of numerical approximations and carry out a theoretical variance reduction analysis. Finally, we illustrate the efficiency of the method through a detailed quantitative assessment.
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Li, Wen. "Numerical methods for the solution of the HJB equations arising in European and American option pricing with proportional transaction costs." University of Western Australia. School of Mathematics and Statistics, 2010. http://theses.library.uwa.edu.au/adt-WU2010.0098.
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This thesis is concerned with the investigation of numerical methods for the solution of the Hamilton-Jacobi-Bellman (HJB) equations arising in European and American option pricing with proportional transaction costs. We first consider the problem of computing reservation purchase and write prices of a European option in the model proposed by Davis, Panas and Zariphopoulou [19]. It has been shown [19] that computing the reservation purchase and write prices of a European option involves solving three different fully nonlinear HJB equations. In this thesis, we propose a penalty approach combined with a finite difference scheme to solve the HJB equations. We first approximate each of the HJB equations by a quasi-linear second order partial differential equation containing two linear penalty terms with penalty parameters. We then develop a numerical scheme based on the finite differencing in both space and time for solving the penalized equation. We prove that there exists a unique viscosity solution to the penalized equation and the viscosity solution to the penalized equation converges to that of the original HJB equation as the penalty parameters tend to infinity. We also prove that the solution of the finite difference scheme converges to the viscosity solution of the penalized equation. Numerical results are given to demonstrate the effectiveness of the proposed method. We extend the penalty approach combined with a finite difference scheme to the HJB equations in the American option pricing model proposed by Davis and Zarphopoulou [20]. Numerical experiments are presented to illustrate the theoretical findings.
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Wang, Wen-Kai. "Application of stochastic differential games and real option theory in environmental economics." Thesis, University of St Andrews, 2009. http://hdl.handle.net/10023/893.
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This thesis presents several problems based on papers written jointly by the author and Dr. Christian-Oliver Ewald. Firstly, the author extends the model presented by Fershtman and Nitzan (1991), which studies a deterministic differential public good game. Two types of volatility are considered. In the first case the volatility of the diffusion term is dependent on the current level of public good, while in the second case the volatility is dependent on the current rate of public good provision by the agents. The result in the latter case is qualitatively different from the first one. These results are discussed in detail, along with numerical examples. Secondly, two existing lines of research in game theoretic studies of fisheries are combined and extended. The first line of research is the inclusion of the aspect of predation and the consideration of multi-species fisheries within classical game theoretic fishery models. The second line of research includes continuous time and uncertainty. This thesis considers a two species fishery game and compares the results of this with several cases. Thirdly, a model of a fishery is developed in which the dynamic of the unharvested fish population is given by the stochastic logistic growth equation and it is assumed that the fishery harvests the fish population following a constant effort strategy. Explicit formulas for optimal fishing effort are derived in problems considered and the effects of uncertainty, risk aversion and mean reversion speed on fishing efforts are investigated. Fourthly, a Dixit and Pindyck type irreversible investment problem in continuous time is solved, using the assumption that the project value follows a Cox-Ingersoll- Ross process. This solution differs from the two classical cases of geometric Brownian motion and geometric mean reversion and these differences are examined. The aim is to find the optimal stopping time, which can be applied to the problem of extracting resources.
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Calcraft, Peter James. "Two-pore channels and NAADP-dependent calcium signalling." Thesis, St Andrews, 2010. http://hdl.handle.net/10023/888.
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Sewambar, Soraya. "The theory of option valuation." Thesis, 1992. http://hdl.handle.net/10413/7830.
Full textAbstract:
Although options have been traded for many centuries, it has remained a relatively
thinly traded financial instrument. Paradoxically, the theory of option
pricing has been studied extensively. This is due to the fact that many of the
financial instruments that are traded in the market place have an option-like
structure, and thus the development of a methodology for option-pricing may
lead to a general methodology for the pricing of these derivative-assets.
This thesis will focus on the development of the theory of option pricing.
Initially, a fundamental principle that underlies the theory of option valuation
will be given. This will be followed by a discussion of the different types
of option pricing models that are prevalent in the literature.
Special attention will then be given to a detailed derivation of both the
Black-Scholes and the Binomial Option pricing models, which will be followed
by a proof of the convergence of the Binomial pricing model to the
Black-Scholes model.
The Black-Scholes model will be adapted to take into account the payment
of dividends, the possibility of a changing inter est rate and the possibility of
a stochastic variance for the rate of return on the underlying as set. Several
applications of the Black-Scholes model will finally be presented.Thesis (M.Sc.)-University of Natal, 1992.
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Choi, Byeongwook. "Numerical methods for the valuation of American options under jump-diffusion processes." Thesis, 2002. http://wwwlib.umi.com/cr/utexas/fullcit?p3099434.
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"Dynamic options portfolio selection." 2003. http://library.cuhk.edu.hk/record=b5891531.
Full textAbstract:
Zhou Xiaozhou.Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.
Includes bibliographical references (leaves 58-59).
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Overview --- p.1
Chapter 1.2 --- Organization Outline --- p.4
Chapter 2 --- Literature Review --- p.5
Chapter 2.1 --- Option --- p.5
Chapter 2.1.1 --- The definition of option --- p.5
Chapter 2.1.2 --- Payoff of Options --- p.6
Chapter 2.1.3 --- Black-Scholes Option Pricing Model --- p.7
Chapter 2.1.4 --- Binomial Model --- p.12
Chapter 2.2 --- Portfolio Theory --- p.15
Chapter 2.2.1 --- The Markowitz Mean-Variance Model --- p.15
Chapter 2.2.2 --- Multi-period Mean-Variance Formulation --- p.17
Chapter 3 --- Multi-Period Options Portfolio Selection Model with Guaran- teed Return --- p.20
Chapter 3.1 --- Problem Formulation --- p.20
Chapter 3.2 --- Solution Algorithm Using Dynamic Programming --- p.25
Chapter 3.3 --- Numerical Example --- p.27
Chapter 4 --- Mean-Variance Formulation of Options Portfolio --- p.36
Chapter 4.1 --- The Problem Formulation --- p.36
Chapter 4.2 --- Solution Algorithm Using Dynamic Programming --- p.39
Chapter 4.3 --- Numerical Example --- p.41
Chapter 5 --- Summary --- p.56
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"A study on options hedge against purchase cost fluctuation in supply contracts." 2008. http://library.cuhk.edu.hk/record=b5893550.
Full textAbstract:
He, Huifen.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.
Includes bibliographical references (leaves 44-48).
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Motivation --- p.1
Chapter 1.2 --- Literature Review --- p.4
Chapter 1.2.1 --- Supply Contracts under Price Uncertainty --- p.5
Chapter 1.2.2 --- Dual Sourcing --- p.6
Chapter 1.2.3 --- Risk Aversion in Inventory Management --- p.6
Chapter 1.2.4 --- Hedging Operational Risk Using Financial Instruments --- p.7
Chapter 1.2.5 --- Financial Literature --- p.9
Chapter 1.3 --- Organization of the Thesis --- p.10
Chapter 2 --- A Risk-Neutral Model --- p.12
Chapter 2.1 --- Framework and Assumptions --- p.12
Chapter 2.2 --- "Price, Forward and Convenience Yield" --- p.14
Chapter 2.2.1 --- Stochastic Model of Price --- p.14
Chapter 2.2.2 --- Marginal Convenience Yield --- p.16
Chapter 2.3 --- Optimality Equations --- p.17
Chapter 2.4 --- The Structure of the Optimal Policy --- p.21
Chapter 2.4.1 --- One-period. Optimal Hedge Decision Rule --- p.21
Chapter 2.4.2 --- One-period Optimal Orderings Decision Rule --- p.23
Chapter 2.4.3 --- Optimal Policy --- p.24
Chapter 3 --- A Risk-Averse Model --- p.28
Chapter 3.1 --- Risk Aversion Modeling and Utility Function --- p.28
Chapter 3.2 --- Multi-Period Inventory Modelling --- p.31
Chapter 3.3 --- Exponential Utility Model --- p.33
Chapter 3.4 --- Optimal Ordering and Hedging Policy for Multi-Period Problem --- p.37
Chapter 4 --- Conclusion and Future Research --- p.40
Bibliography --- p.44
Chapter A --- Appendix --- p.49
Chapter A.l --- Notation --- p.49
Chapter A.2 --- K-Concavity --- p.50
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"Fractional volatility models and malliavin calculus." 2004. http://library.cuhk.edu.hk/record=b5892022.
Full textAbstract:
Ng Chi-Tim.Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.
Includes bibliographical references (leaves 110-114).
Abstracts in English and Chinese.
Chapter Chapter 1 --- Introduction --- p.4
Chapter Chapter 2 --- Mathematical Background --- p.7
Chapter 2.1 --- Fractional Stochastic Integral --- p.8
Chapter 2.2 --- Wick's Calculus --- p.9
Chapter 2.3 --- Malliavin Calculus --- p.19
Chapter 2.4 --- Fractional Ito's Lemma --- p.27
Chapter Chapter 3 --- The Fractional Black Scholes Model --- p.34
Chapter 3.1 --- Fractional Geometric Brownian Motion --- p.35
Chapter 3.2 --- Arbitrage Opportunities --- p.38
Chapter 3.3 --- Fractional Black Scholes Equation --- p.40
Chapter Chapter 4 --- Generalization --- p.43
Chapter 4.1 --- Stochastic Gradients of Fractional Diffusion Processes --- p.44
Chapter 4.2 --- An Example : Fractional Black Scholes Mdel with Varying Trend and Volatility --- p.46
Chapter 4.3 --- Generalization of Fractional Black Scholes PDE --- p.48
Chapter 4.4 --- Option Pricing Problem for Fractional Black Scholes Model with Varying Trend and Volatility --- p.55
Chapter Chapter 5 --- Alternative Fractional Models --- p.59
Chapter 5.1 --- Fractional Constant Elasticity Volatility (CEV) Models --- p.60
Chapter 5.2 --- Pricing an European Call Option --- p.61
Chapter Chapter 6 --- Problems in Fractional Models --- p.66
Chapter Chapter 7 --- Arbitrage Opportunities --- p.68
Chapter 7.1 --- Two Equivalent Expressions for Geometric Brownian Motions --- p.69
Chapter 7.2 --- Self-financing Strategies --- p.70
Chapter Chapter 8 --- Conclusions --- p.72
Chapter Appendix A --- Fractional Stochastic Integral for Deterministic Integrand --- p.75
Chapter A.1 --- Mapping from Inner-Product Space to a Set of Random Variables --- p.76
Chapter A.2 --- Fractional Calculus --- p.77
Chapter A.3 --- Spaces for Deterministic Functions --- p.79
Chapter Appendix B --- Three Approaches of Stochastic Integration --- p.82
Chapter B.1 --- S-Transformation Approach --- p.84
Chapter B.2 --- Relationship between Three Types of Stochastic Integral --- p.89
Reference --- p.90
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"American options pricing with mixed effects model." 2009. http://library.cuhk.edu.hk/record=b5894182.
Full textAbstract:
Ren, You.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.
Includes bibliographical references (leaves 48-51).
Abstract also in Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Background of Option Pricing Theory --- p.1
Chapter 1.2 --- American Option Pricing --- p.3
Chapter 1.3 --- Numerical Approximation of American Option Price --- p.8
Chapter 1.4 --- Statistical Issues --- p.12
Chapter 1.4.1 --- Empirical Calibration --- p.13
Chapter 2 --- Mixed Effects Model for American Option Prices --- p.16
Chapter 2.1 --- Model --- p.16
Chapter 2.2 --- Model Selection --- p.19
Chapter 2.3 --- Empirical Bayes Prediction --- p.21
Chapter 3 --- Simulation and Empirical Data --- p.22
Chapter 3.1 --- Simulation --- p.22
Chapter 3.1.1 --- Simulation of Stock Price Path and a Set of Options --- p.22
Chapter 3.1.2 --- Training Mixed Effects Model --- p.27
Chapter 3.1.3 --- Performance Measure and Prediction Result --- p.30
Chapter 3.2 --- An Application to P&G American Options --- p.36
Chapter 3.2.1 --- The Empirical Data and Setup --- p.36
Chapter 3.2.2 --- Training Mixed Effects Option Pricing Model --- p.37
Chapter 3.2.3 --- Performance Analysis --- p.41
Chapter 4 --- Conclusion and Discussion --- p.46
Bibliography --- p.48
47
"Trading in options: an in-depth analysis." 1999. http://library.cuhk.edu.hk/record=b5889494.
Full textAbstract:
by Fu Yiu-Hang.Thesis (M.B.A.)--Chinese University of Hong Kong, 1999.
Includes bibliographical references (leaves 66-67).
ABSTRACT --- p.ii
TABLE OF CONTENTS --- p.ii
LIST OF TABLES --- p.vi
LIST OF EXHIBITS --- p.vii
PREFACE --- p.viii
ACKNOWLEDGMENTS --- p.x
Chapter
Chapter I. --- INTRODUCTION --- p.1
What is an Option? --- p.1
Options Market --- p.2
Uses of Options --- p.2
Value of Options --- p.3
Index Options --- p.4
Hang Seng Index Options --- p.4
Chapter II. --- BASIC PROPERTIES OF OPTIONS --- p.5
Assumptions --- p.5
Notation --- p.5
Option Prices at Expiration --- p.6
Call Option Prices at Expiration --- p.6
Put Option Prices at Expiration --- p.6
Upper Bounds for Option Prices --- p.6
Upper Bounds for Call Option Prices --- p.6
Upper Bounds for Put Option Prices --- p.6
Lower Bounds for European Option Prices --- p.7
Lower Bounds for European Call Option Prices --- p.7
Lower Bounds for European Put Option Prices --- p.8
Put-Call Parity --- p.8
Chapter III. --- FACTORS AFFECTING OPTION PRICES --- p.10
Price of Underlying Instrument --- p.10
Exercise Price of the Option --- p.10
Volatility of the Price of Underlying Instrument --- p.11
Time to Expiration --- p.11
Risk-free Rate --- p.11
Dividends --- p.12
Chapter IV. --- OPTION PRICING MODEL --- p.13
Assumptions --- p.13
The Price of Underlying Instrument Follows a Lognormal Distribution --- p.13
The Variance of the Rate of Return of Underlying Instrument is a Constant --- p.17
The Risk-free Rate is a Constant --- p.19
No Dividends are Paid --- p.20
There are No Transaction Costs and Taxes --- p.20
The Black-Scholes Option Pricing Model --- p.21
Notation --- p.21
The Formulas --- p.21
The Variables --- p.22
Properties of the Black-Scholes Formulas --- p.22
Implied Volatility --- p.23
Bias of the Black-Scholes Option Pricing Model --- p.26
Other Option Pricing Models。……………… --- p.27
Chapter V. --- SENSITIVITIES OF OPTION PRICE TO ITS FACTORS --- p.29
Delta --- p.29
Vega --- p.30
Theta --- p.31
Rho --- p.32
Gamma --- p.33
Managing the Change in the Value of Option --- p.34
Sensitivities of Portfolio Value to the Factors --- p.34
Chapter VI. --- TRADING STRATEGIES OF OPTIONS --- p.35
Methodology --- p.35
Limitations --- p.36
Basic Strategies --- p.37
Long Call --- p.37
Short Call --- p.39
Long Put --- p.40
Short Put --- p.42
Spread Strategies --- p.43
Money Spread --- p.43
Ratio Spread --- p.46
Box Spread --- p.46
Butterfly Spread --- p.46
Condor --- p.49
Calendar Spread --- p.49
Diagonal Spread --- p.52
Combination Strategies --- p.52
Straddle --- p.52
Strap --- p.54
Strip --- p.54
Strangle --- p.54
Selecting Trading Strategies Intelligently --- p.56
Chapter VII. --- CONCLUSIONS --- p.57
APPENDICES --- p.60
BIBLIOGRAPHY --- p.66
48
"Quanto options under double exponential jump diffusion." 2007. http://library.cuhk.edu.hk/record=b5893201.
Full textAbstract:
Lau, Ka Yung.Thesis (M.Phil.)--Chinese University of Hong Kong, 2007.
Includes bibliographical references (leaves 78-79).
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 2 --- Background --- p.5
Chapter 2.1 --- Jump Diffusion Models --- p.6
Chapter 2.2 --- Double Exponential Jump Diffusion Model --- p.8
Chapter 3 --- Option Pricing with DEJD --- p.10
Chapter 3.1 --- Laplace Transform --- p.10
Chapter 3.2 --- European Option Pricing --- p.13
Chapter 3.3 --- Barrier Option Pricing --- p.14
Chapter 3.4 --- Lookback Options --- p.16
Chapter 3.5 --- Turbo Warrant --- p.17
Chapter 3.6 --- Numerical Examples --- p.26
Chapter 4 --- Quanto Options under DEJD --- p.30
Chapter 4.1 --- Domestic Risk-neutral Dynamics --- p.31
Chapter 4.2 --- The Exponential Copula --- p.33
Chapter 4.3 --- The moment generating function --- p.36
Chapter 4.4 --- European Quanto Options --- p.38
Chapter 4.4.1 --- Floating Exchange Rate Foreign Equity Call --- p.38
Chapter 4.4.2 --- Fixed Exchange Rate Foreign Equity Call --- p.40
Chapter 4.4.3 --- Domestic Foreign Equity Call --- p.42
Chapter 4.4.4 --- Joint Quanto Call --- p.43
Chapter 4.5 --- Numerical Examples --- p.45
Chapter 5 --- Path-Dependent Quanto Options --- p.48
Chapter 5.1 --- The Domestic Equivalent Asset --- p.48
Chapter 5.1.1 --- Mathematical Results on the First Passage Time of the Mixture Exponential Jump Diffusion Model --- p.50
Chapter 5.2 --- Quanto Lookback Option --- p.54
Chapter 5.3 --- Quanto Barrier Option --- p.57
Chapter 5.4 --- Numerical results --- p.61
Chapter 6 --- Conclusion --- p.64
Chapter A --- Numerical Laplace Inversion for Turbo Warrants --- p.66
Chapter B --- The Relation Among Barrier Options --- p.69
Chapter C --- Proof of Lemma 51 --- p.71
Chapter D --- Proof of Theorem 5.4 and 5.5 --- p.74
Bibliography --- p.78
49
"The value of put option to the newsvendor." 2003. http://library.cuhk.edu.hk/record=b5896094.
Full textAbstract:
Guo, Min.Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.
Includes bibliographical references (leaves 66-69).
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 2 --- Notation and Model --- p.8
Chapter 2.1 --- Notation --- p.9
Chapter 2.2 --- Classical News vendor Model --- p.11
Chapter 2.3 --- The Price of the Put Option --- p.12
Chapter 2.4 --- Extended Models with the Option --- p.13
Chapter 3 --- Literature Review --- p.16
Chapter 4 --- Objective I ´ؤ Maximizing Expected Profit --- p.24
Chapter 4.1 --- Single Decision Variable Case: K = Q --- p.24
Chapter 4.2 --- Two Decision Variable Case: K ≤Q --- p.25
Chapter 4.3 --- Summary of the Chapter --- p.28
Chapter 5 --- Objective II ´ؤ Maximizing the Probability of Achieving A Target Profit --- p.30
Chapter 5.1 --- Single Decision Variable Case: K = Q --- p.30
Chapter 5.2 --- Two Decision Variable Case: K ≤ Q --- p.37
Chapter 5.3 --- Numerical Examples --- p.38
Chapter 5.4 --- Summary of the Chapter --- p.41
Chapter 6 --- Objective III ´ؤ Minimizing Profit Variance --- p.43
Chapter 6.1 --- Minimizing Profit Variance through R --- p.44
Chapter 6.2 --- Minimizing Profit Variance through K --- p.51
Chapter 6.2.1 --- Special Case R = s --- p.54
Chapter 6.3 --- Summary of the Chapter --- p.60
Chapter 7 --- Conclusion --- p.63
Bibliography --- p.69
50
"General diffusions: financial applications, analysis and extension." Thesis, 2010. http://library.cuhk.edu.hk/record=b6074923.
Full textAbstract:
General diffusion processes (GDP), or Ito's processes, are potential candidates for the modeling of asset prices, interest rates and other financial quantities to cope with empirical evidence. This thesis considers the applications of general diffusions in finance and potential extensions. In particular, we focus on financial problems involving (optimal) stopping times. A typical example is the valuation of American options. We investigate the use of Laplace-Carson transform (LCT) in valuing American options, and discuss its strengthen and weaknesses. Homotopy analysis from topology is then introduced to derive closed-form American option pricing formulas under GDP. Another example is taken from optimal dividend policies with bankruptcy procedures, which is closely related to excursion time and occupation time of a general diffusion. With the aid of Fourier transform, we further extend the analysis to the case of multi-dimensional GDP by considering the currency option pricing with mean reversion and multi-scale stochastic volatility.Zhao, Jing.
Adviser: Hoi-Ying Wong.
Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: .
Thesis (Ph.D.)--Chinese University of Hong Kong, 2010.
Includes bibliographical references (leaves 97-105).
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 Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstract also in Chinese.