Mean-reverting assets with mean-reverting volatility.

Lo, Yu Wai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.Includes bibliographical references (leaves 66-70).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 2 --- Literature Review --- p.8Chapter 2.1 --- Mean-reverting Model --- p.8Chapter 2.2 --- Volatility Smile --- p.11Chapter 2.3 --- Stochastic Volatility Model --- p.13Chapter 2.4 --- Multiscale Stochastic Volatility Model --- p.15Chapter 3 --- The Heston Stochastic Volatility --- p.17Chapter 3.1 --- The Model --- p.17Chapter 3.1.1 --- The Characteristic Function --- p.18Chapter 3.2 --- European Option Pricing --- p.24Chapter 3.2.1 --- Plain Vanilla Options --- p.25Chapter 3.2.2 --- Implied Volatility --- p.28Chapter 3.2.3 --- Other Payoff Functions --- p.30Chapter 3.3 --- Trinomial Tree: Exotic Option Pricing --- p.31Chapter 3.3.1 --- Sub-tree for the volatility --- p.33Chapter 3.3.2 --- Sub-tree for the asset --- p.34Chapter 3.3.3 --- Non-zero Correlation --- p.37Chapter 3.3.4 --- Calibration to Future prices --- p.38Chapter 3.3.5 --- Numerical Examples --- p.39Chapter 4 --- Multiscale Stochastic Volatility --- p.42Chapter 4.1 --- Model Settings --- p.42Chapter 4.2 --- Pricing --- p.44Chapter 4.3 --- Simulation studies --- p.54Chapter 5 --- Conclusion --- p.59Appendix --- p.61Chapter A --- Verifications --- p.61Chapter A.l --- Proof of Lemma 3.1.1 --- p.61Chapter B --- Black-Scholes Greeks --- p.64Bibliography --- p.6