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
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_327049 |
| Date | January 2010 |
| Contributors | Tang, Sze Ki., Chinese University of Hong Kong Graduate School. Division of Physics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, xiii, 103 leaves : ill. ; 30 cm. |
| Coverage | United States |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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