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1
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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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.
4
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.<br>published_or_final_version<br>Mathematics<br>Doctoral<br>Doctor of Philosophy
5
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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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.<br>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.<br>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.
7
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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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.
9
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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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.
11
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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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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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.
14
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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Chau, Irene. "An empirical comparison using both the term structure of interest rates and alternative models in pricing options on 90-day BAB futures." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 1999. https://ro.ecu.edu.au/theses/1207.
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The use of the term structure of interest rates to price options is relatively new in the literature. It describes the relationship between interest rates and the maturities of bonds. The first model that described the interest rate process was the Vasicek (1977) model. There have been many studies on the formulation of theoretical pricing models. Yet limited empirical research has been done in the area of actually testing the models. In this thesis we report the results of a set of tests of the models indicated below. This paper involves analysis of the pricing errors of the Black model ( 1976), Asay model (1982), Extended-Vasicek model (1990) and Heath-Jarrow-Morton model (HJM) ( 1992) as applied to call options on 90-day Bank Accepted Bill (BAB) futures. Monthly yield curves are generated from cash, futures, swap and interest rate cap data. A number of different methods of analysis are used. These include the use of inferential statistics, non-parametric sign tests and Ordinary Least Square Regressions. The Wilcoxon non-parametric sign test assists the interpretation of whether the pricing errors are from the same distribution. Ordinary Least Square Regressions are used to assess the significance of factors affecting pricing errors. In addition, data are plotted against different variables in order to show any systematic patterns in how pricing errors are affected by the changes in the chosen variables. Monthly options data on BAB futures in the year 1996 suggest that the term structure models have significantly lower pricing errors than the Black and the Asay model. The Heath-Jarrow-Morton model (1992) is overall the better model to use. For the term structure models, pricing errors show a decreasing trend as moneyness increases. The Extended-Vasicek model and the HJM model have significantly lower errors for deep-in the-money and out-of-the-money options. Higher mean absolute errors are observed for at-the-money options for both term structure models. The HJM model overprices at-the money options but underprices in and out-of-the-money options while the Extended Vasicek model underprices deep-in-the-money options but overprices options of other categories. The mean and absolute errors for both the Black model and the Asay model rise as time to maturity and volatility increases. The two models overprice in, at and out-of-the money options and the mean pricing error is lowest for in-the-money options. The results suggest that the factor time to maturity is significant at the 0.05 level to the -mean pricing error for all four models. Moneyness is the only insignificant factor when the Asay model is used. It is also negatively correlated to mean pricing error for the Black model, the Asay model, the Extended-Vasicek model and the HJM model. The R-square for the Extended-Vasicek model was found to be the lowest. Overall, the HJM model gives the lowest pricing error when pricing options on 90-Day Bank Accepted Bill Futures.
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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.<br>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.<br>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.<br>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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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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Soucik, Victor. "Finding the true performance of Australian managed funds." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2002. https://ro.ecu.edu.au/theses/730.
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When making conclusions about the performance of managed funds, it is critical that the framework in which such performance is measured provides an accurate and unbiased environment. In this thesis I search for true performance of the two major classes of funds- equity as well as fixed interest managed funds. Focusing, first on the former class, I examine five measurement models across three risk-free proxies, nine benchmarks proposed by the extant literature (covering conditional and unconditional as well as single and multi factor definitions) and over three independent periods in an effort to identity (in a consistent setting) the most accurate and least biast methodology. I also use the Australian dataset, which inherently mitigates any data biases that may potentially afflict US studies of these methodologies, since these were developed from the same dataset on which they were later tested. Not finding a pre-existing benchmark that is objective yet informative, I develop an independent model that satisfies these, sourcing from fifteen factor candidates across four categories. I find that teaming up a fund based market factor with well-defined proxies for size, value, momentum and conditional dividend yield provides the optimal benchmark. The latter class comprising fixed-interest managed funds is a segment left largely unexplored in the financial literature and neglected outright in the Australian context. I examine three risk-free proxies, six benchmark classes encompassing twenty-one potential factors, across five models and two independent time frames in an effort to establish the most informative and least biased setting. The task is complicated by two issues - an acute lack of Australian data (demanding additional bootstrap simulations and bridging tests with the US markets) and the need for a two-pass (time-series and cross-sectional) analysis, arising from the different information content benchmarks carry in these two dimensions. My results, consistent across time, show that a correct combination of a bond market variable, a mixture of interest rate factors and economic factors as well as the proxy for movements in the equity markets yield the optimal benchmark. Both fund classes point to Jensen's Alpha as the preferred model, but Treynor and Mazuy's definition of a quadratic measure is adequate if timing-selectivity separation is required. Neither class is significantly sensitive to the choice of risk free proxy featuring in the performance measures.
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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.<br>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.<br>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, 2015<br>AFRIKAANSE 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<br>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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Yang, Wenling. "M-GARCH Hedge Ratios And Hedging Effectiveness In Australian Futures Markets." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2000. https://ro.ecu.edu.au/theses/1530.
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This study deals with the estimation of the optimal hedge ratios using various econometric models. Most of the recent papers have demonstrated that the conventional ordinary least squares (OLS) method of estimating constant hedge ratios is inappropriate, other more complicated models however seem to produce no more efficient hedge ratios. Using daily AOIs and SPI futures on the Australian market, optimal hedge ratios are calculated from four different models: the OLS regression model, the bivariate vector autoaggressive model (BVAR), the error-correction model (ECM) and the multivariate diagonal Vcc GARCH Model. The performance of each hedge ratio is then compared. The hedging effectiveness is measured in terms of ex-post and ex-ante risk-return traHe-off at various forcasting horizons. It is generally found that the GARCH time varying hedge ratios provide the greatest portfolio risk reduction, particularly for longer hedging horizons, but hey so not generate the highest portfolio return.
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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.<br>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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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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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.
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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.<p><p>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<p><p>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<p>time-to-maturity.<p><p>In Chapter 4, we use the stochastic dynamic programming approach in order to extend<p>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].<p><p><p><br>Doctorat en Sciences<br>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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"Dynamic options portfolio selection." 2003. http://library.cuhk.edu.hk/record=b5891531.
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Zhou Xiaozhou.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.<br>Includes bibliographical references (leaves 58-59).<br>Abstracts in English and Chinese.<br>Chapter 1 --- Introduction --- p.1<br>Chapter 1.1 --- Overview --- p.1<br>Chapter 1.2 --- Organization Outline --- p.4<br>Chapter 2 --- Literature Review --- p.5<br>Chapter 2.1 --- Option --- p.5<br>Chapter 2.1.1 --- The definition of option --- p.5<br>Chapter 2.1.2 --- Payoff of Options --- p.6<br>Chapter 2.1.3 --- Black-Scholes Option Pricing Model --- p.7<br>Chapter 2.1.4 --- Binomial Model --- p.12<br>Chapter 2.2 --- Portfolio Theory --- p.15<br>Chapter 2.2.1 --- The Markowitz Mean-Variance Model --- p.15<br>Chapter 2.2.2 --- Multi-period Mean-Variance Formulation --- p.17<br>Chapter 3 --- Multi-Period Options Portfolio Selection Model with Guaran- teed Return --- p.20<br>Chapter 3.1 --- Problem Formulation --- p.20<br>Chapter 3.2 --- Solution Algorithm Using Dynamic Programming --- p.25<br>Chapter 3.3 --- Numerical Example --- p.27<br>Chapter 4 --- Mean-Variance Formulation of Options Portfolio --- p.36<br>Chapter 4.1 --- The Problem Formulation --- p.36<br>Chapter 4.2 --- Solution Algorithm Using Dynamic Programming --- p.39<br>Chapter 4.3 --- Numerical Example --- p.41<br>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.
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He, Huifen.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.<br>Includes bibliographical references (leaves 44-48).<br>Abstracts in English and Chinese.<br>Chapter 1 --- Introduction --- p.1<br>Chapter 1.1 --- Motivation --- p.1<br>Chapter 1.2 --- Literature Review --- p.4<br>Chapter 1.2.1 --- Supply Contracts under Price Uncertainty --- p.5<br>Chapter 1.2.2 --- Dual Sourcing --- p.6<br>Chapter 1.2.3 --- Risk Aversion in Inventory Management --- p.6<br>Chapter 1.2.4 --- Hedging Operational Risk Using Financial Instruments --- p.7<br>Chapter 1.2.5 --- Financial Literature --- p.9<br>Chapter 1.3 --- Organization of the Thesis --- p.10<br>Chapter 2 --- A Risk-Neutral Model --- p.12<br>Chapter 2.1 --- Framework and Assumptions --- p.12<br>Chapter 2.2 --- "Price, Forward and Convenience Yield" --- p.14<br>Chapter 2.2.1 --- Stochastic Model of Price --- p.14<br>Chapter 2.2.2 --- Marginal Convenience Yield --- p.16<br>Chapter 2.3 --- Optimality Equations --- p.17<br>Chapter 2.4 --- The Structure of the Optimal Policy --- p.21<br>Chapter 2.4.1 --- One-period. Optimal Hedge Decision Rule --- p.21<br>Chapter 2.4.2 --- One-period Optimal Orderings Decision Rule --- p.23<br>Chapter 2.4.3 --- Optimal Policy --- p.24<br>Chapter 3 --- A Risk-Averse Model --- p.28<br>Chapter 3.1 --- Risk Aversion Modeling and Utility Function --- p.28<br>Chapter 3.2 --- Multi-Period Inventory Modelling --- p.31<br>Chapter 3.3 --- Exponential Utility Model --- p.33<br>Chapter 3.4 --- Optimal Ordering and Hedging Policy for Multi-Period Problem --- p.37<br>Chapter 4 --- Conclusion and Future Research --- p.40<br>Bibliography --- p.44<br>Chapter A --- Appendix --- p.49<br>Chapter A.l --- Notation --- p.49<br>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.
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Ng Chi-Tim.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.<br>Includes bibliographical references (leaves 110-114).<br>Abstracts in English and Chinese.<br>Chapter Chapter 1 --- Introduction --- p.4<br>Chapter Chapter 2 --- Mathematical Background --- p.7<br>Chapter 2.1 --- Fractional Stochastic Integral --- p.8<br>Chapter 2.2 --- Wick's Calculus --- p.9<br>Chapter 2.3 --- Malliavin Calculus --- p.19<br>Chapter 2.4 --- Fractional Ito's Lemma --- p.27<br>Chapter Chapter 3 --- The Fractional Black Scholes Model --- p.34<br>Chapter 3.1 --- Fractional Geometric Brownian Motion --- p.35<br>Chapter 3.2 --- Arbitrage Opportunities --- p.38<br>Chapter 3.3 --- Fractional Black Scholes Equation --- p.40<br>Chapter Chapter 4 --- Generalization --- p.43<br>Chapter 4.1 --- Stochastic Gradients of Fractional Diffusion Processes --- p.44<br>Chapter 4.2 --- An Example : Fractional Black Scholes Mdel with Varying Trend and Volatility --- p.46<br>Chapter 4.3 --- Generalization of Fractional Black Scholes PDE --- p.48<br>Chapter 4.4 --- Option Pricing Problem for Fractional Black Scholes Model with Varying Trend and Volatility --- p.55<br>Chapter Chapter 5 --- Alternative Fractional Models --- p.59<br>Chapter 5.1 --- Fractional Constant Elasticity Volatility (CEV) Models --- p.60<br>Chapter 5.2 --- Pricing an European Call Option --- p.61<br>Chapter Chapter 6 --- Problems in Fractional Models --- p.66<br>Chapter Chapter 7 --- Arbitrage Opportunities --- p.68<br>Chapter 7.1 --- Two Equivalent Expressions for Geometric Brownian Motions --- p.69<br>Chapter 7.2 --- Self-financing Strategies --- p.70<br>Chapter Chapter 8 --- Conclusions --- p.72<br>Chapter Appendix A --- Fractional Stochastic Integral for Deterministic Integrand --- p.75<br>Chapter A.1 --- Mapping from Inner-Product Space to a Set of Random Variables --- p.76<br>Chapter A.2 --- Fractional Calculus --- p.77<br>Chapter A.3 --- Spaces for Deterministic Functions --- p.79<br>Chapter Appendix B --- Three Approaches of Stochastic Integration --- p.82<br>Chapter B.1 --- S-Transformation Approach --- p.84<br>Chapter B.2 --- Relationship between Three Types of Stochastic Integral --- p.89<br>Reference --- p.90
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"American options pricing with mixed effects model." 2009. http://library.cuhk.edu.hk/record=b5894182.
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Ren, You.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.<br>Includes bibliographical references (leaves 48-51).<br>Abstract also in Chinese.<br>Chapter 1 --- Introduction --- p.1<br>Chapter 1.1 --- Background of Option Pricing Theory --- p.1<br>Chapter 1.2 --- American Option Pricing --- p.3<br>Chapter 1.3 --- Numerical Approximation of American Option Price --- p.8<br>Chapter 1.4 --- Statistical Issues --- p.12<br>Chapter 1.4.1 --- Empirical Calibration --- p.13<br>Chapter 2 --- Mixed Effects Model for American Option Prices --- p.16<br>Chapter 2.1 --- Model --- p.16<br>Chapter 2.2 --- Model Selection --- p.19<br>Chapter 2.3 --- Empirical Bayes Prediction --- p.21<br>Chapter 3 --- Simulation and Empirical Data --- p.22<br>Chapter 3.1 --- Simulation --- p.22<br>Chapter 3.1.1 --- Simulation of Stock Price Path and a Set of Options --- p.22<br>Chapter 3.1.2 --- Training Mixed Effects Model --- p.27<br>Chapter 3.1.3 --- Performance Measure and Prediction Result --- p.30<br>Chapter 3.2 --- An Application to P&G American Options --- p.36<br>Chapter 3.2.1 --- The Empirical Data and Setup --- p.36<br>Chapter 3.2.2 --- Training Mixed Effects Option Pricing Model --- p.37<br>Chapter 3.2.3 --- Performance Analysis --- p.41<br>Chapter 4 --- Conclusion and Discussion --- p.46<br>Bibliography --- p.48
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"Trading in options: an in-depth analysis." 1999. http://library.cuhk.edu.hk/record=b5889494.
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by Fu Yiu-Hang.<br>Thesis (M.B.A.)--Chinese University of Hong Kong, 1999.<br>Includes bibliographical references (leaves 66-67).<br>ABSTRACT --- p.ii<br>TABLE OF CONTENTS --- p.ii<br>LIST OF TABLES --- p.vi<br>LIST OF EXHIBITS --- p.vii<br>PREFACE --- p.viii<br>ACKNOWLEDGMENTS --- p.x<br>Chapter<br>Chapter I. --- INTRODUCTION --- p.1<br>What is an Option? --- p.1<br>Options Market --- p.2<br>Uses of Options --- p.2<br>Value of Options --- p.3<br>Index Options --- p.4<br>Hang Seng Index Options --- p.4<br>Chapter II. --- BASIC PROPERTIES OF OPTIONS --- p.5<br>Assumptions --- p.5<br>Notation --- p.5<br>Option Prices at Expiration --- p.6<br>Call Option Prices at Expiration --- p.6<br>Put Option Prices at Expiration --- p.6<br>Upper Bounds for Option Prices --- p.6<br>Upper Bounds for Call Option Prices --- p.6<br>Upper Bounds for Put Option Prices --- p.6<br>Lower Bounds for European Option Prices --- p.7<br>Lower Bounds for European Call Option Prices --- p.7<br>Lower Bounds for European Put Option Prices --- p.8<br>Put-Call Parity --- p.8<br>Chapter III. --- FACTORS AFFECTING OPTION PRICES --- p.10<br>Price of Underlying Instrument --- p.10<br>Exercise Price of the Option --- p.10<br>Volatility of the Price of Underlying Instrument --- p.11<br>Time to Expiration --- p.11<br>Risk-free Rate --- p.11<br>Dividends --- p.12<br>Chapter IV. --- OPTION PRICING MODEL --- p.13<br>Assumptions --- p.13<br>The Price of Underlying Instrument Follows a Lognormal Distribution --- p.13<br>The Variance of the Rate of Return of Underlying Instrument is a Constant --- p.17<br>The Risk-free Rate is a Constant --- p.19<br>No Dividends are Paid --- p.20<br>There are No Transaction Costs and Taxes --- p.20<br>The Black-Scholes Option Pricing Model --- p.21<br>Notation --- p.21<br>The Formulas --- p.21<br>The Variables --- p.22<br>Properties of the Black-Scholes Formulas --- p.22<br>Implied Volatility --- p.23<br>Bias of the Black-Scholes Option Pricing Model --- p.26<br>Other Option Pricing Models。……………… --- p.27<br>Chapter V. --- SENSITIVITIES OF OPTION PRICE TO ITS FACTORS --- p.29<br>Delta --- p.29<br>Vega --- p.30<br>Theta --- p.31<br>Rho --- p.32<br>Gamma --- p.33<br>Managing the Change in the Value of Option --- p.34<br>Sensitivities of Portfolio Value to the Factors --- p.34<br>Chapter VI. --- TRADING STRATEGIES OF OPTIONS --- p.35<br>Methodology --- p.35<br>Limitations --- p.36<br>Basic Strategies --- p.37<br>Long Call --- p.37<br>Short Call --- p.39<br>Long Put --- p.40<br>Short Put --- p.42<br>Spread Strategies --- p.43<br>Money Spread --- p.43<br>Ratio Spread --- p.46<br>Box Spread --- p.46<br>Butterfly Spread --- p.46<br>Condor --- p.49<br>Calendar Spread --- p.49<br>Diagonal Spread --- p.52<br>Combination Strategies --- p.52<br>Straddle --- p.52<br>Strap --- p.54<br>Strip --- p.54<br>Strangle --- p.54<br>Selecting Trading Strategies Intelligently --- p.56<br>Chapter VII. --- CONCLUSIONS --- p.57<br>APPENDICES --- p.60<br>BIBLIOGRAPHY --- p.66
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"Quanto options under double exponential jump diffusion." 2007. http://library.cuhk.edu.hk/record=b5893201.
Full textAbstract:
Lau, Ka Yung.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2007.<br>Includes bibliographical references (leaves 78-79).<br>Abstracts in English and Chinese.<br>Chapter 1 --- Introduction --- p.1<br>Chapter 2 --- Background --- p.5<br>Chapter 2.1 --- Jump Diffusion Models --- p.6<br>Chapter 2.2 --- Double Exponential Jump Diffusion Model --- p.8<br>Chapter 3 --- Option Pricing with DEJD --- p.10<br>Chapter 3.1 --- Laplace Transform --- p.10<br>Chapter 3.2 --- European Option Pricing --- p.13<br>Chapter 3.3 --- Barrier Option Pricing --- p.14<br>Chapter 3.4 --- Lookback Options --- p.16<br>Chapter 3.5 --- Turbo Warrant --- p.17<br>Chapter 3.6 --- Numerical Examples --- p.26<br>Chapter 4 --- Quanto Options under DEJD --- p.30<br>Chapter 4.1 --- Domestic Risk-neutral Dynamics --- p.31<br>Chapter 4.2 --- The Exponential Copula --- p.33<br>Chapter 4.3 --- The moment generating function --- p.36<br>Chapter 4.4 --- European Quanto Options --- p.38<br>Chapter 4.4.1 --- Floating Exchange Rate Foreign Equity Call --- p.38<br>Chapter 4.4.2 --- Fixed Exchange Rate Foreign Equity Call --- p.40<br>Chapter 4.4.3 --- Domestic Foreign Equity Call --- p.42<br>Chapter 4.4.4 --- Joint Quanto Call --- p.43<br>Chapter 4.5 --- Numerical Examples --- p.45<br>Chapter 5 --- Path-Dependent Quanto Options --- p.48<br>Chapter 5.1 --- The Domestic Equivalent Asset --- p.48<br>Chapter 5.1.1 --- Mathematical Results on the First Passage Time of the Mixture Exponential Jump Diffusion Model --- p.50<br>Chapter 5.2 --- Quanto Lookback Option --- p.54<br>Chapter 5.3 --- Quanto Barrier Option --- p.57<br>Chapter 5.4 --- Numerical results --- p.61<br>Chapter 6 --- Conclusion --- p.64<br>Chapter A --- Numerical Laplace Inversion for Turbo Warrants --- p.66<br>Chapter B --- The Relation Among Barrier Options --- p.69<br>Chapter C --- Proof of Lemma 51 --- p.71<br>Chapter D --- Proof of Theorem 5.4 and 5.5 --- p.74<br>Bibliography --- p.78
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"The value of put option to the newsvendor." 2003. http://library.cuhk.edu.hk/record=b5896094.
Full textAbstract:
Guo, Min.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.<br>Includes bibliographical references (leaves 66-69).<br>Abstracts in English and Chinese.<br>Chapter 1 --- Introduction --- p.1<br>Chapter 2 --- Notation and Model --- p.8<br>Chapter 2.1 --- Notation --- p.9<br>Chapter 2.2 --- Classical News vendor Model --- p.11<br>Chapter 2.3 --- The Price of the Put Option --- p.12<br>Chapter 2.4 --- Extended Models with the Option --- p.13<br>Chapter 3 --- Literature Review --- p.16<br>Chapter 4 --- Objective I ´ؤ Maximizing Expected Profit --- p.24<br>Chapter 4.1 --- Single Decision Variable Case: K = Q --- p.24<br>Chapter 4.2 --- Two Decision Variable Case: K ≤Q --- p.25<br>Chapter 4.3 --- Summary of the Chapter --- p.28<br>Chapter 5 --- Objective II ´ؤ Maximizing the Probability of Achieving A Target Profit --- p.30<br>Chapter 5.1 --- Single Decision Variable Case: K = Q --- p.30<br>Chapter 5.2 --- Two Decision Variable Case: K ≤ Q --- p.37<br>Chapter 5.3 --- Numerical Examples --- p.38<br>Chapter 5.4 --- Summary of the Chapter --- p.41<br>Chapter 6 --- Objective III ´ؤ Minimizing Profit Variance --- p.43<br>Chapter 6.1 --- Minimizing Profit Variance through R --- p.44<br>Chapter 6.2 --- Minimizing Profit Variance through K --- p.51<br>Chapter 6.2.1 --- Special Case R = s --- p.54<br>Chapter 6.3 --- Summary of the Chapter --- p.60<br>Chapter 7 --- Conclusion --- p.63<br>Bibliography --- p.69
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"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.<br>Zhao, Jing.<br>Adviser: Hoi-Ying Wong.<br>Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: .<br>Thesis (Ph.D.)--Chinese University of Hong Kong, 2010.<br>Includes bibliographical references (leaves 97-105).<br>Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.<br>Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.<br>Abstract also in Chinese.