This thesis studies the problems of semistatic trading strategies in a discrete-time financial market, where stocks are traded dynamically and European options at maturity are traded statically. First, we show that pointwise limits of semistatic trading strategies are again semistatic strategies. The analysis is carried out in full generality for a two-period model, and under a probabilistic condition for multi-period, multi-stock models. Our result contrasts with a counterexample of Acciaio, Larsson and Schachermayer, and shows that their observation is due to a failure of integrability rather than instability of the semistatic form. Mathematically, our results relate to the decomposability of functions as studied in the context of Schrödinger bridges. Second, we study the so-called martingale Schrödinger bridge 𝑄⁎ in a two-period financial market; that is, the minimal-entropy martingale measure among all models calibrated to option prices. This minimization is shown to be in duality with an exponential utility maximization over semistatic portfolios. Under a technical condition on the physical measure 𝑃, we show that an optimal portfolio exists and provides an explicit solution for 𝑄⁎. Specifically, we exhibit a dense subset of calibrated martingale measures with particular properties to show that the portfolio in question has a well-defined and integrable option position.

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General diffusion processes (GDP), or Ito's processes, are potential candidates for the modeling of asset prices, interest rates and other financial quantities to cope with empirical evidence. This thesis considers the applications of general diffusions in finance and potential extensions. In particular, we focus on financial problems involving (optimal) stopping times. A typical example is the valuation of American options. We investigate the use of Laplace-Carson transform (LCT) in valuing American options, and discuss its strengthen and weaknesses. Homotopy analysis from topology is then introduced to derive closed-form American option pricing formulas under GDP. Another example is taken from optimal dividend policies with bankruptcy procedures, which is closely related to excursion time and occupation time of a general diffusion. With the aid of Fourier transform, we further extend the analysis to the case of multi-dimensional GDP by considering the currency option pricing with mean reversion and multi-scale stochastic volatility. / Zhao, Jing. / Adviser: Hoi-Ying Wong. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 97-105). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

When pricing American-style options on d assets by Monte Carlo methods, one usually stores the simulated asset prices at all time steps on all paths in order to determine when to exercise the options. If N time steps and M paths are used; then the storage requirement is d · M · N. In this thesis, we give two simulation methods to price multi-asset American-style options, where the storage requirement only grows like (d + 1)M + N. The only additional computational cost is that we have to generate each random number twice instead of once. For machines with limited memory, we can now use larger values of M and N to improve the accuracy in pricing the options. / by Wong Chi Yan. / Adviser: Raymond H. Chan. / Source: Dissertation Abstracts International, Volume: 70-03, Section: B, page: 1708. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 79-82). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

by Veronica Ho Pui Kwan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 99-103). / Prologue --- p.1 / Chapter Essay I: --- Examination of the GARCH Option Pricing Model in the case of Hang Seng Index Option / Chapter 1. --- Introduction --- p.4 / Chapter 2. --- Holes' in the Black-Scholes Model --- p.7 / Chapter 3. --- A Big 'Hole' -- Varying Volatility --- p.14 / Chapter 4. --- A Remedy : the GARCH Option Pricing Model --- p.31 / Chapter 5. --- Research Methodology and Data --- p.38 / Chapter 6. --- Empirical Results --- p.50 / Chapter 7. --- Conclusion --- p.67 / Chapter Essay II: --- Barrier Options / Chapter 1. --- Introduction on Barrier Option --- p.70 / Chapter 2. --- Pricing Models --- p.74 / Chapter 3. --- Hedging of Barrier Option --- p.81 / Chapter 4. --- Examination of a Down-and-Out Put Option --- p.88 / References --- p.99

by Wan Chi-Keung. / Thesis (M.B.A.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 33-34). / TABLE OF CONTENTS / ABSTRACT --- p.ii / TABLE OF CONTENTS --- p.iii / LIST OF FIGURES --- p.iv / LIST OF TABLE --- p.v / ACKNOWLEDGEMENT --- p.vi / Chapter / Chapter I. --- INTRODUCTION --- p.1 / Chapter II. --- VOLATILITY SMILE --- p.4 / The Black- Scholes Model --- p.6 / The Implied Tree --- p.7 / The Implied Probability Distribution --- p.10 / Chapter III. --- LITERATURE REVIEW --- p.12 / Chapter IV. --- RECOVERING PROBABILITY DISTRIBUTIONS OF HSI --- p.18 / Shimko's Method --- p.19 / Data Selection --- p.22 / Probability Distributions of HSI --- p.23 / Chapter V. --- CONLUDING REMARKS --- p.27 / APPENDIX --- p.30 / BIBLIOGRAPHY --- p.33

Thesis (PhD)--Macquarie University, Division of Economic and Financial Studies, Dept. of Statistics, 2008. / Bibliography: p. 73-77.

Thesis (M.B.A.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 107-109).

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.

Ho Kin Fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 71-73). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Motivation --- p.3 / Chapter 1.3 --- Chapter Layout --- p.5 / Chapter 1.4 --- Summary --- p.7 / Chapter 2 --- Literature Review --- p.11 / Chapter 2.1 --- Implied Asset Return Distribution --- p.13 / Chapter 2.2 --- The Jarrow-Rudd Skewness and Kurtosis-Adjusted Model --- p.16 / Chapter 2.3 --- Implied Moments in Asset Return Distribution --- p.24 / Chapter 2.4 --- Summary --- p.26 / Chapter 3 --- Methodology --- p.28 / Chapter 3.1 --- Application to the Nikkei Index Options --- p.28 / Chapter 3.2 --- In-Sample Parameters Estimation --- p.31 / Chapter 3.3 --- Out-Sample Prediction Error Evaluation --- p.34 / Chapter 3.4 --- Time-Series Movements of Higher Moments --- p.35 / Chapter 3.5 --- Summary --- p.37 / Chapter 4 --- Empirical Results --- p.38 / Chapter 4.1 --- In-Sample Parameters Estimation --- p.38 / Chapter 4.2 --- The Out-Sample Prediction Error Evaluation --- p.43 / Chapter 4.3 --- Time Series Movements of Higher Moments --- p.45 / Chapter 4.4 --- Implications --- p.55 / Chapter 4.5 --- Summary --- p.57 / Chapter 5 --- Conclusions --- p.59 / Chapter A --- Additional Figures --- p.62