In part 1 of this study I examine several models of competitive markets in which a group of uninformed traders uses the equilibrium price of a traded asset as an indirect source of information known to a group of informed traders. Four different models are compared in two homogeneous information cases plus one asymmetric information case, revealing a) an allocative efficiency benefit resulting from the opportunity to trade current consumption for future consumption, b) a 'dealer' benefit accruing to traders who are able to observe and act on demand fluctuations not apparent to other traders, c) a 'hedging' benefit accruing to all traders, and d) a loss of hedging benefits due to information dissemination before hedge trading can take place. The effect of an increase in precision of information given to informed traders is calculated for the above factors and for net welfare. In part 2, a two-factor model using the instantaneous rate of interest and the return on a consol bond to describe the term structure of interest rates - the Brennan-Schwartz model - is used to derive theoretical prices for American call and put options on U.S. government bonds and treasury bills. These model prices are then compared with market prices. The theoretical model used to value the debt options also provides hedge ratios which may be used to construct zero-investment portfolios which, in theory, are perfectly riskless. Several trading strategies based on these 'riskless' portfolios are examined. / Business, Sauder School of / Graduate

常方差彈性(CEV) 模型能夠刻畫波動率微笑的優點使之成為期權定價中的實用工具，然而它在應用到美式衍生工具時面臨分析上及計算上的挑戰。現行的解析方法是對代表著期權價格函數和其最佳履約曲線的自由邊界問題進行拉普拉斯卡森變換(LCT) ，繼而獲得在此變換下的解析解，可是此解含有合流超線幾何函數，使得它的數值計算在某些參數下顯得不穩定及低效。本文運用漸近法徹底解決美式期權在常方差彈性模型下的定價問題，並用永久性和限時性的美式看跌期權作為例子闡述所提出的方法。 / The constant elasticity of variance (CEV) model is a practical approach to option pricing by fitting to the implied volatility skew. Its application to American-style derivatives, however, poses analytical and numerical challenges. By taking the Laplace Carson transform (LCT) to the free-boundary value problem characterizing the option value function and the early exercise boundary, the analytical result involves confluent hyper-geometric functions. Thus, the numerical computation could be unstable and inefficient for certain set of parameter values. We solve this problem by an asymptotic approach to the American option pricing problem under the CEV model. We demonstrate the use of the proposed approach using perpetual and finite-time American puts. / Detailed summary in vernacular field only. / Pun, Chi Seng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 39-40). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Problem Formulation --- p.4 / Chapter 2.1 --- The CEV model --- p.4 / Chapter 2.2 --- The free-boundary value problem --- p.5 / Chapter 2.2.1 --- Perpetual American put --- p.5 / Chapter 2.2.2 --- Finite-time American put --- p.6 / Chapter 3 --- Asymptotic expansion of American put --- p.8 / Chapter 3.1 --- Perpetual American put --- p.8 / Chapter 3.2 --- Finite-time American put --- p.16 / Chapter 4 --- Numerical examples --- p.24 / Chapter 4.1 --- Perpetual American put --- p.24 / Chapter 4.2 --- Finite-time American put --- p.26 / Chapter 5 --- Conclusion --- p.29 / Chapter A --- Proof of Lemma 3.1 --- p.30 / Chapter B --- Property of ak --- p.32 / Chapter C --- Explicit formulas for u₂(S) --- p.34 / Chapter D --- Closed-form solutions --- p.37 / Bibliography --- p.40

Tang, Sze Ki = 計算美式賣權的最優提早履約邊界及期權金 / 鄧思麒. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 96-102). / Abstracts in English and Chinese. / Tang, Sze Ki = Ji suan Mei shi mai quan de zui you ti zao lu yue bian jie ji qi quan jin / Deng Siqi. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Black-Scholes Option Pricing Model --- p.1 / Chapter 1.1.1 --- Geometric Brownian Motion --- p.1 / Chapter 1.1.2 --- The Black-Scholes Equation --- p.3 / Chapter 1.1.3 --- The European Put Option --- p.5 / Chapter 1.1.4 --- The American Put Option --- p.7 / Chapter 1.1.5 --- Perpetual American Option --- p.9 / Chapter 1.2 --- Literature Review --- p.9 / Chapter 1.2.1 --- Direct Numerical Method --- p.10 / Chapter 1.2.2 --- Analytical Approximation --- p.11 / Chapter 1.2.3 --- Analytical Representation --- p.12 / Chapter 1.2.4 --- Mean-Reverting Lognormal Process --- p.13 / Chapter 1.2.5 --- Constant Elasticity of Variance Process --- p.15 / Chapter 1.2.6 --- Model Parameters with Time Dependence --- p.17 / Chapter 1.3 --- Overview --- p.18 / Chapter 2 --- Mean-Reverting Lognormal Model --- p.21 / Chapter 2.1 --- Moving Barrier Rebate Options under GBM --- p.21 / Chapter 2.2 --- Simulating American Puts under GBM --- p.25 / Chapter 2.3 --- Special Case: Time Independent Parameters --- p.26 / Chapter 2.3.1 --- Reduction to Ingersoll's Approximations --- p.26 / Chapter 2.3.2 --- Perpetual American Put Option --- p.28 / Chapter 2.4 --- Moving Barrier Rebate Options under MRL Process --- p.29 / Chapter 2.4.1 --- Reduction to Black-Scholes Model --- p.30 / Chapter 2.5 --- Simulating the American Put under MRL Process --- p.32 / Chapter 3 --- Constant Elasticity of Variance Model --- p.34 / Chapter 3.1 --- Transformations --- p.35 / Chapter 3.2 --- Homogeneous Solution on a Semi-Infinite Domain --- p.37 / Chapter 3.3 --- Particular Solution on a Semi-Infinite Domain --- p.38 / Chapter 3.4 --- Moving Barrier Options with Rebates --- p.39 / Chapter 3.5 --- Simulating the American Options --- p.40 / Chapter 3.6 --- Implication from the Special Case L = 0 --- p.41 / Chapter 4 --- Optimization for the Approximation --- p.43 / Chapter 4.1 --- Introduction --- p.43 / Chapter 4.2 --- The Optimization Scheme --- p.44 / Chapter 4.2.1 --- Illustrative Examples --- p.44 / Chapter 4.3 --- Discussion --- p.45 / Chapter 4.3.1 --- Upper Bound of the Exact Early Exercise Price --- p.45 / Chapter 4.3.2 --- Tightest Lower Bound of the American Put Option Price --- p.48 / Chapter 4.3.3 --- Ingersoll's Early Exercise Decision Rule --- p.51 / Chapter 4.3.4 --- Connection between Ingersoll's Rule and Samuelson's Smooth Paste Condition --- p.51 / Chapter 4.3.5 --- Computation Efficiency --- p.52 / Chapter 4.4 --- Robustness Analysis --- p.53 / Chapter 4.4.1 --- MRL Model --- p.53 / Chapter 4.4.2 --- CEV Model --- p.55 / Chapter 4.5 --- Conclusion --- p.57 / Chapter 5 --- Multi-stage Approximation Scheme --- p.59 / Chapter 5.1 --- Introduction --- p.59 / Chapter 5.2 --- Multistage Approximation Scheme for American Put Options --- p.60 / Chapter 5.3 --- Black-Scholes GBM Model --- p.61 / Chapter 5.3.1 --- "Stage 1: Time interval [0, t1]" --- p.61 / Chapter 5.3.2 --- "Stage 2: Time interval [t1, T]" --- p.62 / Chapter 5.4 --- Mean Reverting Lognormal Model --- p.63 / Chapter 5.4.1 --- "Stage 1: Time interval [0, t1]" --- p.63 / Chapter 5.4.2 --- "Stage 2: Time interval [t1, T]" --- p.64 / Chapter 5.5 --- Constant Elasticity of Variance Model --- p.66 / Chapter 5.5.1 --- "Stage 1: Time interval [0, t1]" --- p.66 / Chapter 5.5.2 --- "Stage 2: Time interval [t1, T]" --- p.67 / Chapter 5.6 --- Duration of Time Intervals --- p.69 / Chapter 5.7 --- Discussion --- p.72 / Chapter 5.7.1 --- Upper Bounds for the Optimal Early Exercise Prices --- p.73 / Chapter 5.7.2 --- Error Analysis --- p.74 / Chapter 5.8 --- Conclusion --- p.77 / Chapter 6 --- Numerical Analysis --- p.79 / Chapter 6.1 --- Sensitivity Analysis of American Put Options in MRL Model --- p.79 / Chapter 6.1.1 --- Volatility --- p.79 / Chapter 6.1.2 --- Risk-free Interest Rate and Dividend Yield --- p.80 / Chapter 6.1.3 --- Speed of Mean Reversion --- p.81 / Chapter 6.1.4 --- Mean Underlying Asset Price --- p.83 / Chapter 6.2 --- Sensitivity Analysis of American Put Options in CEV Model --- p.85 / Chapter 6.2.1 --- Elasticity Factor --- p.87 / Chapter 6.3 --- American Options with time-dependent Volatility --- p.87 / Chapter 6.3.1 --- MRL American Options --- p.89 / Chapter 6.3.2 --- CEV American Options --- p.90 / Chapter 6.3.3 --- Discussion --- p.91 / Chapter 7 --- Conclusion --- p.94 / Bibliography --- p.96 / Chapter A --- Derivation of The Duhamel Superposition Integral --- p.101 / Chapter A.1 --- Time Independent Inhomogeneous Boundary Value Problem --- p.101 / Chapter A.2 --- Time Dependent Inhomogeneous Boundary Value Problem --- p.102