Computing the optimal early exercise boundary and the premium for American put options.

• Other Authors: Tang, Sze Ki.
• Format: Others
• Language: English; Chinese
• Published: 2010
• Subjects: Options (Finance) > Mathematical models; Options (Finance) > United States > Mathematical models; Boundary value problems
• Online Access: http://library.cuhk.edu.hk/record=b5894314; http://repository.lib.cuhk.edu.hk/en/item/cuhk-327049

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