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Dissertations / Theses on the topic 'Options (Finance) – Prices – Mathematical models'
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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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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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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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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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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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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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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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Oagile, Joel. "Sequential Calibration of Asset Pricing Models to Option Prices." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29840.
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This paper implements four calibration methods on stochastic volatility models. We estimate the latent state and parameters of the models using three non-linear filtering methods, namely the extended Kalman filter (EKF), iterated extended Kalman filter (IEKF) and the unscented Kalman filter (UKF). A simulation study is performed and the non-linear filtering methods are compared to the standard least square method (LSQ). The results show that both methods are capable of tracking the hidden state and time varying parameters with varying success. The non-linear filtering methods are faster and generally perform better on validation. To test the stability of the parameters, we carry out a delta hedging study. This exercise is not only of interest to academics, but also to traders who have to hedge their positions. Our results do not show any significant benefits resulting from performing delta hedging using parameter estimates obtained from non-linear filtering methods as compared to least square parameter estimates.
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Cheng, Xin. "Three essays on volatility forecasting." HKBU Institutional Repository, 2010. http://repository.hkbu.edu.hk/etd_ra/1183.
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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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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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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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Blix, Magnus. "Essays in mathematical finance : modeling the futures price." Doctoral thesis, Handelshögskolan i Stockholm, Finansiell Ekonomi (FI), 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:hhs:diva-534.
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This thesis consists of four papers dealing with the futures price process. In the first paper, we propose a two-factor futures volatility model designed for the US natural gas market, but applicable to any futures market where volatility decreases with maturity and varies with the seasons. A closed form analytical expression for European call options is derived within the model and used to calibrate the model to implied market volatilities. The result is used to price swaptions and calendar spread options on the futures curve. In the second paper, a financial market is specified where the underlying asset is driven by a d-dimensional Wiener process and an M dimensional Markov process. On this market, we provide necessary and, in the time homogenous case, sufficient conditions for the futures price to possess a semi-affine term structure. Next, the case when the Markov process is unobservable is considered. We show that the pricing problem in this setting can be viewed as a filtering problem, and we present explicit solutions for futures. Finally, we present explicit solutions for options on futures both in the observable and unobservable case. The third paper is an empirical study of the SABR model, one of the latest contributions to the field of stochastic volatility models. By Monte Carlo simulation we test the accuracy of the approximation the model relies on, and we investigate the stability of the parameters involved. Further, the model is calibrated to market implied volatility, and its dynamic performance is tested. In the fourth paper, co-authored with Tomas Björk and Camilla Landén, we consider HJM type models for the term structure of futures prices, where the volatility is allowed to be an arbitrary smooth functional of the present futures price curve. Using a Lie algebraic approach we investigate when the infinite dimensional futures price process can be realized by a finite dimensional Markovian state space model, and we give general necessary and sufficient conditions, in terms of the volatility structure, for the existence of a finite dimensional realization. We study a number of concrete applications including the model developed in the first paper of this thesis. In particular, we provide necessary and sufficient conditions for when the induced spot price is a Markov process. We prove that the only HJM type futures price models with spot price dependent volatility structures, generically possessing a spot price realization, are the affine ones. These models are thus the only generic spot price models from a futures price term structure point of view.Diss. Stockholm : Handelshögskolan, 2004
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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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Yuen, Fei-lung, and 袁飛龍. "Pricing options and equity-indexed annuities in regime-switching models by trinomial tree method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B45595616.
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Hao, Fangcheng, and 郝方程. "Options pricing and risk measures under regime-switching models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B4714726X.
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Cheng, Lap-yan, and 鄭立仁. "Extension of price-trend models with applications in finance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B37428408.
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任尚智 and Sheung-chi Phillip Yam. "Algebraic methods on some problems in finance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B3122698X.
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Merino, Fernández Raúl. "Option Price Decomposition for Local and Stochastic Volatility Jump Diffusion Models." Doctoral thesis, Universitat de Barcelona, 2021. http://hdl.handle.net/10803/671682.
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In this thesis, an option price decomposition for local and stochastic volatility jump diffusion models is studied. On the one hand, we generalise and extend the Alòs decomposition to be used in a wide variety of models such as a general stochastic volatility model, a stochastic volatility jump dffusion model with finite activity or a rough volatility model.
Furthermore, we note that in the case of local volatility models, speci_cally, spot-dependent models, a new decomposition formula must be used to obtain good numerical results. In particular, we study the CEV model. On the other hand, we observe that the approximation formula can be improved by using the decomposition formula recursively. Using this decomposition method, the call price can be transformed into a Taylor type formula containing an infinite series with stochastic terms. New approximation formulae are obtained in the Heston model case, finding better approximations.En aquesta tesi, s'estudia una descomposició del preu d'una opció per a models de volatilitat local i volatilitat estocàstica amb salts. D'una banda, generalitzem i estenem la descomposició d'Alòs per a ser utilitzada en una àmplia varietat de models com, per exemple, un model de volatilitat estocàstica general, un model de volatilitat estocàstica amb salts d'activitat finita o un model de volatilitat 'rough'. A més a més, veiern que en el cas dels models de volatilitat local, en particular, els models dependents del 'spot' s'ha d'utilitzar una nova fórmula de descomposició per a obtenir bons resultats numèrics. En particular, estudiem el model CEV. D'altra banda, observem que la fórmula d'aproximació es pot millorar utilitzant la formula de descomposició de forma recursiva. Mitjançant aquesta tècnica de descomposició, el preu d'una opció de compra es pot transformar en una formula tipus Taylor que conté una sèrie infinita de termes estocàstics. S'obtenen noves fórmules d'aproximació en el cas del model de Heston, trobant una millor aproximació.
En esta tesis, se estudia una descomposición del precio de una opción para los modelos de volatilidad local y volatilidad estocástica con saltos. Por un lado, generalizamos y ampliamos la descomposición de Alòs para ser utilizada en una amplia variedad de modelos como, por ejemplo, un modelo de volatilidad estocástica general, un modelo de volatilidad estocástica con saltos de actividad finita o un modelo de volatilidad 'rough'. Además, vemos que en el caso de los modelos de volatilidad local, en particular, los modelos dependientes del 'spot', se debe utilizar una nueva fórmula de descomposición para obtener buenos resultados numéricos. En particular, estudiamos el modelo CEV. Por otro lado, observamos que la fórmula de aproximación se puede mejorar utilizando la fórmula de descomposición de forma recursiva. Mediante esta técnica de descomposición, el precio de una opción de compra se puede transformar en una fórmula tipo Taylor que contiene una serie infinita de términos estocásticos. Se obtienen nuevas fórmulas de aproximación en el caso del modelo de Heston, encontrando una mejor aproximación.
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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.
Full textAbstract:
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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Wei, Yong, and 卫勇. "The real effects of S&P 500 Index additions: evidence from corporate investment." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B4490681X.
Full text
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Arroyo, Jorge M. "Money and the dispersion of relative prices in the drug and apparel industries." Thesis, Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/28574.
Full text
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Nhongo, Tawuya D. R. "Pricing exotic options using C++." Thesis, Rhodes University, 2007. http://hdl.handle.net/10962/d1008373.
Full textAbstract:
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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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.
Full textAbstract:
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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Gleeson, Cameron Banking & Finance Australian School of Business UNSW. "Pricing and hedging S&P 500 index options : a comparison of affine jump diffusion models." Awarded by:University of New South Wales. School of Banking and Finance, 2005. http://handle.unsw.edu.au/1959.4/22379.
Full textAbstract:
This thesis examines the empirical performance of four Affine Jump Diffusion models in pricing and hedging S&P 500 Index options: the Black Scholes (BS) model, Heston???s Stochastic Volatility (SV) model, a Stochastic Volatility Price Jump (SVJ) model and a Stochastic Volatility Price-Volatility Jump (SVJJ) model. The SVJJ model structure allows for simultaneous jumps in price and volatility processes, with correlated jump size distributions. To the best of our knowledge this is the first empirical study to test the hedging performance of the SVJJ model. As part of our research we derive the SVJJ model minimum variance hedge ratio. We find the SVJ model displays the best price prediction. The SV model lacks the structural complexity to eliminate Black Scholes pricing biases, whereas our results indicate the SVJJ model suffers from overfitting. Despite significant evidence from in and out-of-sample pricing that the SV and SVJ models were better specified than the BS model, this did not result in an improvement in dynamic hedging performance. Overall the BS delta hedge and SV minimum variance hedge produced the lowest errors, although their performance across moneyness-maturity categories differed greatly. The SVJ model???s results were surprisingly poor given its superior performance in out-of-sample pricing. We attribute the inadequate performance of the jump models to the lower hedging ratios these models provided, which may be a result of the negative expected jump sizes.
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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.
Full textAbstract:
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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Ysusi, Mendoza Carla Mariana. "Estimation of the variation of prices using high-frequency financial data." Thesis, University of Oxford, 2005. http://ora.ox.ac.uk/objects/uuid:1b520271-2a63-428d-b5a0-e7e9c4afdc66.
Full textAbstract:
When high-frequency data is available, realised variance and realised absolute variation can be calculated from intra-day prices. In the context of a stochastic volatility model, realised variance and realised absolute variation can estimate the integrated variance and the integrated spot volatility respectively. A central limit theory enables us to do filtering and smoothing using model-based and model-free approaches in order to improve the precision of these estimators. When the log-price process involves a finite activity jump process, realised variance estimates the quadratic variation of both continuous and jump components. Other consistent estimators of integrated variance can be constructed on the basis of realised multipower variation, i.e., realised bipower, tripower and quadpower variation. These objects are robust to jumps in the log-price process. Therefore, given adequate asymptotic assumptions, the difference between realised multipower variation and realised variance can provide a tool to test for jumps in the process. Realised variance becomes biased in the presence of market microstructure effect, meanwhile realised bipower, tripower and quadpower variation are more robust in such a situation. Nevertheless there is always a trade-off between bias and variance; bias is due to market microstructure noise when sampling at high frequencies and variance is due to the asymptotic assumptions when sampling at low frequencies. By subsampling and averaging realised multipower variation this effect can be reduced, thereby allowing for calculations with higher frequencies.
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Hoffmeyer, Allen Kyle. "Small-time asymptotics of call prices and implied volatilities for exponential Lévy models." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/53506.
Full textAbstract:
We derive at-the-money call-price and implied volatility asymptotic expansions in time to maturity for a selection of exponential Lévy models, restricting our attention to asset-price models whose log returns structure is a Lévy process. We consider two main problems. First, we consider very general Lévy models that are in the domain of attraction of a stable random variable. Under some relatively minor assumptions, we give first-order at-the-money call-price and implied volatility asymptotics. In the case where our Lévy process has Brownian component, we discover new orders of convergence by showing that the rate of convergence can be of the form t¹/ᵃℓ(t) where ℓ is a slowly varying function and $\alpha \in (1,2)$. We also give an example of a Lévy model which exhibits this new type of behavior where ℓ is not asymptotically constant. In the case of a Lévy process with Brownian component, we find that the order of convergence of the call price is √t. Second, we investigate the CGMY process whose call-price asymptotics are known to third order. Previously, measure transformation and technical estimation methods were the only tools available for proving the order of convergence. We give a new method that relies on the Lipton-Lewis formula, guaranteeing that we can estimate the call-price asymptotics using only the characteristic function of the Lévy process. While this method does not provide a less technical approach, it is novel and is promising for obtaining second-order call-price asymptotics for at-the-money options for a more general class of Lévy processes.
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Gong, Ruoting. "Small-time asymptotics and expansions of option prices under Levy-based models." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44798.
Full textAbstract:
This thesis is concerned with the small-time asymptotics and expansions of call option prices, when the log-return processes of the underlying stock prices follow several Levy-based models. To be specific, we derive the time-to-maturity asymptotic behavior for both at-the-money (ATM), out-of-the-money (OTM) and in-the-money (ITM) call-option prices under several jump-diffusion models and stochastic volatility models with Levy jumps. In the OTM and ITM cases, we consider a general stochastic volatility model with independent Levy jumps, while in the ATM case, we consider the pure-jump CGMY model with or without an independent Brownian component.
An accurate modeling of the option market and asset prices requires a mixture of a continuous diffusive component and a jump component. In this thesis, we first model the log-return process of a risk asset with a jump diffusion model by combining a stochastic volatility model with an independent pure-jump Levy process. By assuming
smoothness conditions on the Levy density away from the origin and a small-time large deviation principle on the stochastic volatility model, we derive the small-time expansions, of arbitrary polynomial order, in time-t, for the tail distribution of the log-return process, and for the call-option price which is not at-the-money. Moreover, our approach allows for a unified treatment of more general payoff functions. As a
consequence of our tail expansions, the polynomial expansion in t of the transition
density is also obtained under mild conditions.
The asymptotic behavior of the ATM call-option prices is more complicated to obtain, and, in general, is given by fractional powers of t, which depends on different choices of the underlying log-return models. Here, we focus on the CGMY model, one of the most popular tempered stable models used in financial modeling. A novel
second-order approximation for ATM option prices under the pure-jump CGMY Levy model is derived, and then extended to a model with an additional independent Brownian component. The third-order asymptotic behavior of the ATM option prices as
well as the asymptotic behavior of the corresponding Black-Scholes implied volatilities
are also addressed.
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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
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"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
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"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
50
"A numerical method for American option pricing under CEV model." 2007. http://library.cuhk.edu.hk/record=b5893177.
Full textAbstract:
Zhao Jing.Thesis (M.Phil.)--Chinese University of Hong Kong, 2007.
Includes bibliographical references (leaves 72-74).
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 2 --- The Constant Elasticity of Variance Model --- p.6
Chapter 2.1 --- The CEV Assumption --- p.7
Chapter 2.2 --- Properties of the CEV Model --- p.9
Chapter 2.3 --- Empirical Evidence and Theoretical Support --- p.11
Chapter 3 --- Option Pricing under CEV --- p.14
Chapter 3.1 --- The Valuation of European Options --- p.14
Chapter 3.2 --- The Valuation of American Options --- p.17
Chapter 3.3 --- "How ""far"" is Enough?" --- p.19
Chapter 4 --- The Proposed Artificial Boundary Approach --- p.21
Chapter 4.1 --- Standardized Form of the CEV Model --- p.21
Chapter 4.2 --- Exact Artificial Boundary Conditions --- p.23
Chapter 4.3 --- The Integral Kernels and Numerical Laplace Inversion --- p.31
Chapter 5 --- Numerical Examples --- p.35
Chapter 5.1 --- General Numerical Scheme --- p.35
Chapter 6 --- Homotopy Analysis Method --- p.47
Chapter 6.1 --- The Front-Fixing Transformation --- p.47
Chapter 6.2 --- Homotopy Analysis Method --- p.49
Chapter 6.2.1 --- Zero-order Deformation Equation --- p.50
Chapter 6.2.2 --- High-order Deformation Equation --- p.54
Chapter 6.2.3 --- Pade Technique --- p.57
Chapter 6.3 --- Numerical Comparison --- p.58
Chapter 7 --- Conclusion --- p.63
Appendix --- p.65
Chapter A --- The Valuation of Perpetual American Options --- p.65
Chapter B --- "Derivation of G(Y,r) = Ls-1 ((Y/a)vKv(Y)/sKv(sa)" --- p.66
Chapter C --- Numerical Laplace Inversion --- p.68
Bibliography --- p.72