The purpose of this study is to investigate the daily return behavior of underlying common stocks in the period surrounding the option expiration date. A second purpose is to determine the variables that may be causing the differential capital market effect across firms. The hypothesis of a negative return effect in the expiration week followed by a positive effect in the subsequent week is tested first. It is shown that this pattern should be expected due to the enhanced opportunity for and profitability of position unwinding, arbitrage and manipulation activity as the expiration date approached. The study period covers 32 expiration periods from 1978 through 1981 and involves a sample of 138 underlying stocks. The study employs the market model for generating abnormal returns on a daily basis. The results support the hypothesis and in particular show that the most significant negative return behavior occurs on Thursday and Friday of the expiration week. The second phase of the study correlates, via a cross-sectional multiple regression model, the suggested expiration induced events of position unwinding, arbitrage and manipulation activities with the return behavior of the underlying stocks. It is hypothesized that those common stocks which exhibit the greatest negative returns in the expiration week are those stocks and related call options that are most heavily involved in position unwinding, arbitrage and manipulation activities. Trading volume in both the underlying stock and the options is suggested as a surrogate for these three activities. Therefore, volume is negatively related to underlying stock returns. Two additional explanatory variables of the expiration week returns are included in the regression model. A negative relationship is hypothesized if options are dually listed and a positive relationship if puts are traded. The results of the tests generally support these hypothesized functional relationships. The study concludes that, although significant abnormal returns and explanatory variables are found, the magnitudes are probably not large enough to profitably exploit after paying transaction and search costs. As puts trading appears to offset the market inefficiencies caused by call option trading, the concern of regulators that options trading unduly affects stock prices seems unwarranted.

This study is a test of the efficiency of the London Traded Options Market. Because it uses the Black-Scholes Option Pricing Model, it is also a test of option pricing. In the process of examining call option price behaviour it investigates the effects of three empirical factors. First, it investigates the effect of a non-constant share price volatility. Hitherto, there has been no agreed procedure on modelling or forecasting the future share price volatility. This study shows that the GARCH process has the best forecasting accuracy. The ex ante GARCH volatility estimate is then incorporated in the Black-Scholes model. Because the volatility is assumed constant in the Black-Scholes model, the consideration of adapting the GARCH volatility into the model sheds insight on bridging empirical results and theoretical requirements. Second, because the London Traded Options Market is thinly traded the quoted prices may not reflect prices at which trade did or could take place. However, information on call option trading volume may not be available. This study develops and implements an analytical criterion to select the most actively traded call options. The call options selected by this criterion bear the basic characteristics of those frequently traded call options where trading volume is available. Third, this study uses the bid and ask quotations for shares and call options to test the efficiency of the London Traded Options Market. By incorporating the bid-ask spread directly in the establishment of arbitrage portfolios, an accurate assessment of transactions data can be made. The results of incorporating these factors in the test for market efficiency reveal that, despite the identification of mispriced call options, it would not have been possible to exploit the mispricing by setting up arbitrage portfolios. It must therefore be concluded that the London Traded Options Market was trading efficiently over the period of this study.

We consider the numerical solution of discretised Hamilton-Jacobi-Bellman (HJB) equations with applications in finance. For the discrete linear complementarity problem arising in American option pricing, we study a policy iteration method. We show, analytically and numerically, that, in standard situations, the computational cost of this approach is comparable to that of European option pricing. We also characterise the shortcomings of policy iteration, providing a lower bound for the number of steps required when having inaccurate initial data. For discretised HJB equations with a finite control set, we propose a penalty approach. The accuracy of the penalty approximation is of first order in the penalty parameter, and we present a Newton-type iterative solver terminating after finitely many steps with a solution to the penalised equation. For discretised HJB equations and discretised HJB obstacle problems with compact control sets, we also introduce penalty approximations. In both cases, the approximation accuracy is of first order in the penalty parameter. We again design Newton-type methods for the solution of the penalised equations. For the penalised HJB equation, the iterative solver has monotone global convergence. For the penalised HJB obstacle problem, the iterative solver has local quadratic convergence. We carefully benchmark all our numerical schemes against current state-of-the-art techniques, demonstrating competitiveness.

Financial mathematics is a branch of mathematics that assesses the risk and value of various financial instruments. Banks, companies, and other institutions mitigate their risk through financial instruments known as derivatives,that derive their value from some underlying asset. The equations that arise from pricing and modeling can be very complex, leading to the necessity of numerical methods. This project studied the use of certain numerical methods for the pricing of a particular type of option called an Asian option. Asian options can provide favorable risk profiles because the payout is determined based on the average value over a time period, rather than the final value. The price of an Asian option is governed by a partial differential equation in three variables: stock price, average price over the current time interval, and time. The solution method was first to discretize the partial differential equation into a system of ordinary differential equations. Next, the ODE system was integrated using a stiff-ODE solver available in MATLAB. Enhancements to this solution method include specifying the sparsity pattern, implementing an iterative linear solver (GMRES) in place of MATLAB's built-in direct linear solver, and using preconditioning to improve the solution characteristics of that solver.

by Lee Yiu Cho. / Thesis (M.B.A.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaf 47). / ACKNOWLEDGMENT --- p.iii / ABSTRACT --- p.iv / TABLE OF CONTENTS --- p.v / LIST OF CHARTS --- p.vi / Chapter / Chapter I. --- INTRODUCTION --- p.1 / Chapter II. --- THE HANG SENG INDEX OPTION --- p.3 / Chapter III. --- LITERATURE REVIEW --- p.6 / Chapter IV. --- METHODOLOGY & DATA COLLECTION --- p.9 / Methodology --- p.9 / The Black-Scholes Model --- p.9 / Data Collection --- p.11 / Data Manipulation --- p.13 / Limitation of Data --- p.14 / Chapter V. --- EMPIRICAL RESULTS --- p.16 / General Trading Pattern --- p.16 / Comparison of Actual and Theoretical Premiums --- p.17 / Analysis for 2 Sub-periods --- p.19 / Correlation Between Deviations and Variables --- p.22 / The Degree of in-the-money or out-of-the-money --- p.22 / Actual Premium Level --- p.23 / Transaction Volume --- p.25 / Chapter VI. --- CONCLUSION --- p.26 / CHARTS --- p.29 / BIBLIOGRAPHY --- p.47

by Mok Man-fai, Mansfield. / Thesis (M.B.A.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 49-50. / ABSTRACT --- p.i / ACKNOWLEDGEMENT --- p.ii / TABLE OF CONTENTS --- p.iii / Chapter / Chapter I. --- INTRODUCTION --- p.1 / Chapter II. --- EURODOLLAR FUTURES AND OPTIONS --- p.3 / Eurodollar Futures --- p.3 / Hedging With Eurodollar Futures --- p.4 / Options On Eurodollar Futures --- p.5 / Contract Type --- p.5 / Contract Style --- p.6 / Contract Lifespan --- p.6 / Contract Value --- p.6 / Hedging With Eurodollar Options --- p.7 / Naked Positions --- p.7 / Chapter III. --- ASSET/LIABILITY MANAGEMENT --- p.9 / Gap Concept --- p.10 / Gap Analysis --- p.11 / Types of Gaps --- p.12 / Positive And Negative Gaps --- p.13 / Voluntary And Involuntary Gaps --- p.13 / Chapter IV. --- HEDGING THE GAP --- p.14 / Macro Hedge --- p.14 / Micro Hedge --- p.17 / Macro Hedge vs Micro Hedge --- p.17 / Chapter V. --- HEDGING METHODOLOGY --- p.19 / Cross Hedge Basis Risk --- p.20 / Hedge Ratio --- p.20 / Time Basis Risk . . --- p.21 / Basic Hedge With No Time Basis Risk --- p.23 / Example 1: Single 90-Day Gap --- p.24 / Example 2: Single 30-Day Gap --- p.24 / Example 3: Single 180-Day Gap --- p.25 / Example 4: Series of 90-day gaps --- p.25 / Example 5: Series of 30-Day Gaps --- p.26 / Basic Hedge With Time Basis Risk --- p.27 / Hedging Of A Series Of Liability Issues --- p.32 / Strip hedge --- p.32 / Stack hedge --- p.33 / Chapter VI. --- OPTIONS AND FUTURES --- p.35 / Similarities and Differences --- p.35 / Merits And Demerits --- p.37 / Chapter VII. --- REASONS FOR HEDGING --- p.39 / Merits --- p.39 / Demerits --- p.40 / Chapter VIII. --- THE SITUATION IN HONG KONG --- p.42 / Chapter IX. --- CONCLUSION --- p.45 / APPENDIX --- p.47 / BIBLIOGRAPHY --- p.49

Heung Ling-lung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 81-82). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgements --- p.iv / Chapter Chapter1: --- Introduction --- p.1 / Chapter Chapter2: --- Review of binomial schemes and trinomial schemes --- p.4 / Chapter Chapter3: --- Binomial/trinomial scheme from the viewpoint of quadrature --- p.12 / Chapter Chapter4: --- Binomial/trinomial schemes from Gaussian quadrature formula --- p.16 / Chapter Chapter5: --- New Schemes from other quadrature formula --- p.27 / Chapter Chapter6: --- Multinomial scheme --- p.35 / Chapter Chapter7: --- Numerical results --- p.41 / Chapter Chapter8: --- Conclusion --- p.47 / Appendix --- p.49 / Bibliography --- p.81

實證證據顯示商品價格有均值回歸和跳躍的特性。由於一些商品期權收益涉及歷史商品價格的算術平均，因此我們求出算術亞式期權在均值回歸跳躍擴散過程下的分析解。比分析解是對資產價格最終值和實際平均值的聯合特徽函數進行快速傅立葉變換獲得。我們通過數值模擬研究來檢驗此建議方法的準確度和計算效率。 / Empirical evidence indicates that commodity prices are mean reverting and exhibit jumps. As some commodity option payoff involves the arithmetic average of historical commodity prices, we derive an analytical solution to arithmetic Asian options under a mean reverting jump diffusion process. The analytical solution is implemented with the fast Fourier transform based on the joint characteristic function of the terminal asset price and the realized average value. We also examine the accuracy and computational efficiency of the proposed method through numerical studies. / Detailed summary in vernacular field only. / Chung, Shing Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 40-42). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Model with constant parameters --- p.5 / Chapter 2.1 --- Model specification --- p.6 / Chapter 2.2 --- Joint characteristic function --- p.8 / Chapter 3 --- Model with time-dependent parameters --- p.12 / Chapter 3.1 --- Model specification --- p.13 / Chapter 3.2 --- Joint characteristic function --- p.13 / Chapter 4 --- Fast Fourier transform on Asian option prices --- p.18 / Chapter 5 --- Numerical results --- p.20 / Chapter 5.1 --- Comparison of the analytical solution and Monte Carlo simulation . --- p.20 / Chapter 5.2 --- Price sensitivity and model parameters --- p.26 / Chapter 5.3 --- Price sensitivity and payoff structure --- p.26 / Chapter 6 --- Conclusion --- p.33 / Chapter A --- Normally distributed jump size --- p.34 / Bibliography --- p.40

針對Lévy過程下的二維期權定價問題，本文提出了一種基於快速傅利葉變換(FFT)的解決方案，稱之為二維快速傅利葉變換網絡。不論是時間從屬還是線性組合，此方法適用於所有能取得聯合特徵函數的二維Lévy構建。快速傅利葉變換的種種優點使得比數值方法在不影響結果精確性的前提下，大大降低了所需計算時間。理論上，更高維的Lévy期權定價問題也可以通過擴展數值網絡解決。除此之外，我們還探究了資產波動性亦服從Lévy過程的單資產期權定價。這種資產價值和波動性由一組相關Lévy過程驅動的模型被稱為時間轉換Lévy過程。最後，關於美式及奇異期權定價的數值算例驗證了文中方法的準確性和有效性。 / We propose a two-dimensional network to retrieve the price of two-asset option under Lévy processes by using the fast Fourier transform (FFT). It can be applied to different multivariate Lévy constructions such as subordination and linear combination provided that the joint characteristic function is obtainable. With the prevalent implementation of FFT, the network approach results in significant computational time reduction while maintaining satisfactory accuracy. In general, multi-dimensional option pricing problems are also solvable by extending this network. Furthermore, we investigate option pricing on a single asset where the asset return and its volatility are driven by a pair of dependent Lévy processes. Such a model is also called the random time-changed Lévy process. Numerical examples are given to demonstrate the efficiency and accuracy of FFT-network applied to exotic and American-style options. / Detailed summary in vernacular field only. / Wang, Weiyin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 41-43). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / List of Tables --- p.ii / List of Figures --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.4 / Chapter 2.1 --- Lévy Process --- p.4 / Chapter 2.1.1 --- Definition and Properties --- p.4 / Chapter 2.1.2 --- Multivariate Lévy Construction --- p.6 / Chapter 2.2 --- Fast Fourier Transform (FFT) in Option Pricing --- p.9 / Chapter 2.2.1 --- European Option on One Asset --- p.9 / Chapter 2.2.2 --- European Option on Two Assets --- p.11 / Chapter 3 --- Two-dimensional FFT-network Model --- p.13 / Chapter 3.1 --- Two-dimensional FFT-network --- p.15 / Chapter 3.2 --- Two-asset Option Pricing --- p.22 / Chapter 3.2.1 --- General Model --- p.22 / Chapter 3.2.2 --- Specific Models --- p.23 / Chapter 3.3 --- Random Time-changed Lévy Process --- p.25 / Chapter 3.3.1 --- Model --- p.26 / Chapter 3.3.2 --- Correlation Adjustment --- p.28 / Chapter 4 --- Numerical Examples --- p.31 / Chapter 4.1 --- Two-asset Option --- p.31 / Chapter 4.1.1 --- Spread Option Pricing --- p.31 / Chapter 4.1.2 --- Pricing under Diffierent Multivariate Lévy Constructions --- p.36 / Chapter 4.2 --- One-asset Option under Random Time-changed Lévy Process --- p.37 / Chapter 5 --- Conclusion --- p.40 / Bibliography --- p.41

有各式各樣的參數與非參數期貨定價模型被廣泛應用於金融領域。其中一些模型的組合能顯著提升期貨定價的準確性。更具體的說，可以先通過參數模型擬合數據，再使用非參數模型學習並修正誤差估價誤差。本論文作為范和Mancini(2009) 結果的延伸，將市場交易的歐式期權價格作為輸入數據，運用「有參數模型指導的非參數定價方法」對障礙期權進行估價。「自動誤差修正估價法」運用非參數方法對由參數估價法產生的誤差進行修正，使得障礙期權的非參數定價模型可以被視為一系列的歐式期權定價的組合。在整個障礙期權的估價過程中，本論文同時提供了一種分數階快速傅裡葉變換的應用，可通過由非參數方法獲得的標的資產對數的存活函數計算標的資產對數最大值分佈的特徵函數。 / There are a variety of parametric and nonparametric option pricing models commonly used in Finance. A combination of them can enhance the pricing performance significantly. Specifically, one proposes to fit the data with a parametric method and then correct the pricing errors empirically with a nonparametric learning approach. This thesis extends Fan and Mancini's (2009) model-guided nonparametric method to barrier option pricing using market traded European option data. Adopting automatic correction of errors (ACE) method to estimate the risk neutral conditional survivor function, by which the pricing error of the initial parametric estimates is captured nonparametrically, enables the nonparametric pricing procedure to value a barrier option as a sum of sequence of European options. As a byproduct from the valuation process, this thesis also provides a modified fractional fast Fourier transform technique compute the characteristic function of the running maximum log-price of the underlying asset nonparametrically through the calibrated survivor functions. / Detailed summary in vernacular field only. / Chi, Chengzhan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 38-39). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Nonparametric Local Regression Modelling --- p.4 / Chapter 2.1 --- Function Estimation by Local Constant --- p.4 / Chapter 2.2 --- Function Estimation by Local Linear Regression --- p.5 / Chapter 3 --- Nonparametric ACE European Option Pricing --- p.7 / Chapter 3.1 --- European Option Prices and Risk Neutral Survivor Functions --- p.7 / Chapter 3.2 --- Estimation of Risk Neutral Survivor Functions --- p.10 / Chapter 3.2.1 --- Risk Neutral Survivor Functions and Traded Options --- p.10 / Chapter 3.2.2 --- Survivor Function Estimation with Nonparametric ACE Method --- p.11 / Chapter 3.3 --- Representation of European Option Prices at Log-asset Level and Numerical Example --- p.15 / Chapter 4 --- Nonparametric ACE Barrier Option Pricing Framework --- p.20 / Chapter 4.1 --- Continuous-time Barrier Option --- p.20 / Chapter 4.2 --- Discrete Approximation and Backward Induction --- p.21 / Chapter 4.3 --- Decomposed Problems --- p.25 / Chapter 5 --- Nonparametric Estimation of Cumulative Distribution Function of M{U+2C7C}(R{U+209C}) --- p.28 / Chapter 5.1 --- Survivor Functions and Maxima Probabilities --- p.28 / Chapter 5.2 --- Characteristic Functions of Maxima --- p.30 / Chapter 5.2.1 --- Algorithm --- p.30 / Chapter 5.2.2 --- Preparation --- p.31 / Chapter 5.2.3 --- Fast Fourier Transform (FFT) --- p.31 / Chapter 5.2.4 --- Fractional Fast Fourier Transform (FRFT) --- p.33 / Chapter 5.2.5 --- Derivation of ΦR{U+209C} --- p.34 / Chapter 5.3 --- Numerical Experiments --- p.35 / Chapter 6 --- Conclusion --- p.37 / Bibliography --- p.38