by Matthew Bailey Greenberg, Ng Hin Wah. / Thesis (M.B.A.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 61-62). / ABSTRACT --- p.ii / TABLE OF CONTENTS --- p.iv / Chapter / Chapter I. --- INTRODUCTION --- p.1 / Chapter II. --- CONVERTIBLE BONDS AND WARRANTS --- p.3 / ConvertIBle Bonds --- p.3 / Value At Maturity --- p.5 / Value Before Maturity --- p.6 / Warrants --- p.8 / The Difference Between Convertible Bonds and Warrants --- p.11 / Considerations of Issuing Convertibles and Bond with Warrants --- p.13 / Valuation of Convertible Bond --- p.15 / Valuation of Warrants --- p.18 / Chapter III. --- CALLABLE BONDS --- p.20 / Performance Characteristics of Callable Bonds --- p.21 / Valuation of a Two-year Callable Bond with the Salomon Brothers Model --- p.22 / Valuation of a Three-year Callable Bond with the Salomon Brothers Model --- p.25 / Step1: Determination of ru and rd --- p.27 / "Step 2: Determination of ruu, rud and rdd " --- p.28 / "Black, Derman & Toy Model (BDT) " --- p.30 / Step 1: Determination of ru and rd --- p.31 / "Step 2: Determination of ruu, rud and rdd " --- p.32 / Chapter IV. --- SINKING-FUND BONDS --- p.37 / Advantages for the Investor --- p.38 / Disadvantages for the Investor --- p.38 / Methods Used by Issuers for Early Bond Redemption --- p.39 / Valuation of Non-callable Sinking Fund Bonds --- p.40 / Valuation of Callable Sinking Fund Bond --- p.45 / Chapter V. --- VALUATION OF A CALLABLE BOND BY A COMPUTERIZED PROGRAM… --- p.47 / System requirements --- p.48 / Opening the program file --- p.48 / Manual for using the program --- p.48 / Construction of Interest Rate Tree --- p.48 / Valuation of a Callable Bond --- p.50 / APPENDIX --- p.55 / BIBLIOGRAPHY --- p.61

Wu, Tao. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 56-61). / Abstracts in English and Chinese. / Chapter 1 --- Background and Organization --- p.7 / Chapter 2 --- Parallel Talbot method for solving partial integro- differential equations --- p.9 / Chapter 2.1 --- Introduction --- p.9 / Chapter 2.2 --- Initial-boundary value problem --- p.11 / Chapter 2.3 --- Spatial discretization and semidiscrete problem --- p.12 / Chapter 2.4 --- Parallel Talbot method --- p.15 / Chapter 2.4.1 --- Φ-functions and Talbot quadrature --- p.15 / Chapter 2.4.2 --- Control on nonnormality and feasibility con- straints --- p.18 / Chapter 2.4.3 --- Optimal parameterization of parabolic Talbot contour --- p.22 / Chapter 2.5 --- Numerical experiments --- p.26 / Chapter 2.6 --- Conclusion --- p.32 / Chapter 3 --- Memory-reduction Monte Carlo method for pricing American options --- p.37 / Chapter 3.1 --- Introduction --- p.37 / Chapter 3.2 --- Exponential Levy processes and the full-storage method --- p.39 / Chapter 3.3 --- Random number generators --- p.41 / Chapter 3.4 --- The memory-reduction method --- p.43 / Chapter 3.5 --- Numerical examples --- p.45 / Chapter 3.5.1 --- Black-Scholes model --- p.46 / Chapter 3.5.2 --- Merton's jump-diffusion model --- p.48 / Chapter 3.5.3 --- Variance gamma model --- p.50 / Chapter 3.5.4 --- Remarks on the efficiency of the memory-reduction method --- p.52 / Chapter 3.6 --- Conclusion --- p.53 / Chapter 3.7 --- Appendix --- p.54

Cheng, Ping. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 91-96). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.1.1 --- Accumulator in a Nutshell --- p.1 / Chapter 1.1.2 --- Criticism over Accumulators --- p.3 / Chapter 1.1.3 --- Significance of Research over Accumulators --- p.4 / Chapter 1.1.4 --- Contribution of this Research --- p.5 / Chapter 1.2 --- Literature Review --- p.6 / Chapter 1.2.1 --- Literature on Option Pricing Theory --- p.6 / Chapter 1.2.2 --- Literature on Occupation Time Derivatives and Accumulators --- p.9 / Chapter 1.2.3 --- Accumulators as Occupation Time Deriva- tives --- p.14 / Chapter 1.3 --- Structure of this Thesis --- p.16 / Chapter 2 --- Theoretical Foundation --- p.17 / Chapter 2.1 --- Black Scholes Framework --- p.18 / Chapter 2.1.1 --- The Model --- p.18 / Chapter 2.1.2 --- Girsanov's Theorem --- p.20 / Chapter 2.1.3 --- Simulation --- p.21 / Chapter 2.2 --- Heston Framework --- p.22 / Chapter 2.2.1 --- Motivation to Extend to Heston Model --- p.22 / Chapter 2.2.2 --- The Model --- p.23 / Chapter 2.2.3 --- The Monte Carlo Method --- p.25 / Chapter 3 --- Pricing under Black-Scholes Framework --- p.30 / Chapter 3.1 --- Structure One (Suspension Feature) --- p.30 / Chapter 3.1.1 --- Introduction --- p.30 / Chapter 3.1.2 --- Model --- p.32 / Chapter 3.1.3 --- Sensitivity Tests --- p.35 / Chapter 3.1.4 --- Simulation Results --- p.38 / Chapter 3.2 --- Structure Two (Knock-out Feature) --- p.40 / Chapter 3.2.1 --- Introduction --- p.40 / Chapter 3.2.2 --- Model --- p.41 / Chapter 3.2.3 --- Sensitivity Tests --- p.45 / Chapter 3.2.4 --- Simulation Results --- p.48 / Chapter 3.3 --- Structure Three (Knock-out & Double Commit- ment Feature) --- p.50 / Chapter 3.3.1 --- Introduction --- p.50 / Chapter 3.3.2 --- Model --- p.51 / Chapter 3.3.3 --- Sensitivity Tests --- p.56 / Chapter 3.3.4 --- Simulation Results --- p.58 / Chapter 4 --- Extension: Pricing under Heston Framework --- p.59 / Chapter 4.1 --- Structure One --- p.59 / Chapter 4.1.1 --- Pricing of the Contract --- p.59 / Chapter 4.2 --- Structure Two and Three --- p.61 / Chapter 4.2.1 --- Simulation Results --- p.62 / Chapter 4.3 --- Heston Parameters Estimates --- p.63 / Chapter 5 --- Discussion --- p.66 / Chapter 5.1 --- Volatility of Accumulators --- p.66 / Chapter 5.2 --- Instability in the Model Parameters --- p.69 / Chapter 5.3 --- Premium over Accumulators --- p.71 / Chapter 5.4 --- Return of the Accumulator Products --- p.72 / Chapter 6 --- Future Work & Conclusion --- p.75 / Chapter 6.1 --- Future Work --- p.75 / Chapter 6.2 --- Conclusion --- p.76 / Chapter A --- Other Parameters Estimation --- p.77 / Chapter B --- Sample Contracts --- p.80 / Chapter B.1 --- Equity Accumulator --- p.80 / Chapter B.2 --- Commodity Accumulator --- p.80 / Chapter B.3 --- FX-Linked Accumulation --- p.80 / Bibliography --- p.91

This thesis considers the effect of stochastic skew in the interest rate cap and currency option markets, where we observe obvious stochastic variation of skew of implied volatility curve over time. To develop option pricing models consistent with empirical evidence, we adopt the Wishart process to model both stochastic volatility and stochastic skew of the asset return and to price options in both markets. As an affine model, the model is analytically tractable. Some distributional properties of the models are studied. The key feature of our model is that, when compared with the multi-factor Heston model, which generates stochastic skew through its volatility processes, the Wishart process contains not only volatility processes, but also volatility-unrelated processes which provide extra freedom to model the variation of skew that is not captured by the volatility processes. Numerical experiments demonstrate that the Wishart model has greater flexibility to model stochastic skew than the multi-factor Heston model in both the interest rate cap market and currency option market. Finally, results of calibration to market data and model estimation demonstrate the superiority of the Wishart model to the multi-factor Heston model in the interest rate cap market. / Ng, Hon Yip. / Advisers: Kwai-Sun Leung; Duan Li. / Source: Dissertation Abstracts International, Volume: 73-09(E), Section: A. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 89-98). / 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 dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

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.

University of Macau / Faculty of Science and Technology / Department of Mathematics

Not available / text

This paper studies the influence on the Japanese stock (cash and futures) markets of the Nikkei put warrants which were traded in Toronto and New York from February 1989 to April 1993. Implied changes in the Japanese prices based on the previous days’ North American warrant prices are compared to the actual price changes. Special attention is placed on the period from January 1990 to August 1992 when the Japanese stock market had a major decline.

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.

This paper studies the influence on the Japanese stock (cash and futures) markets of the Nikkei put warrants which were traded in Toronto and New York from February 1989 to April 1993. Implied changes in the Japanese prices based on the previous days’ North American warrant prices are compared to the actual price changes. Special attention is placed on the period from January 1990 to August 1992 when the Japanese stock market had a major decline. / Business, Sauder School of / Graduate