Fractional volatility models and malliavin calculus.

Ng Chi-Tim.Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.Includes bibliographical references (leaves 110-114).Abstracts in English and Chinese.Chapter Chapter 1 --- Introduction --- p.4Chapter Chapter 2 --- Mathematical Background --- p.7Chapter 2.1 --- Fractional Stochastic Integral --- p.8Chapter 2.2 --- Wick's Calculus --- p.9Chapter 2.3 --- Malliavin Calculus --- p.19Chapter 2.4 --- Fractional Ito's Lemma --- p.27Chapter Chapter 3 --- The Fractional Black Scholes Model --- p.34Chapter 3.1 --- Fractional Geometric Brownian Motion --- p.35Chapter 3.2 --- Arbitrage Opportunities --- p.38Chapter 3.3 --- Fractional Black Scholes Equation --- p.40Chapter Chapter 4 --- Generalization --- p.43Chapter 4.1 --- Stochastic Gradients of Fractional Diffusion Processes --- p.44Chapter 4.2 --- An Example : Fractional Black Scholes Mdel with Varying Trend and Volatility --- p.46Chapter 4.3 --- Generalization of Fractional Black Scholes PDE --- p.48Chapter 4.4 --- Option Pricing Problem for Fractional Black Scholes Model with Varying Trend and Volatility --- p.55Chapter Chapter 5 --- Alternative Fractional Models --- p.59Chapter 5.1 --- Fractional Constant Elasticity Volatility (CEV) Models --- p.60Chapter 5.2 --- Pricing an European Call Option --- p.61Chapter Chapter 6 --- Problems in Fractional Models --- p.66Chapter Chapter 7 --- Arbitrage Opportunities --- p.68Chapter 7.1 --- Two Equivalent Expressions for Geometric Brownian Motions --- p.69Chapter 7.2 --- Self-financing Strategies --- p.70Chapter Chapter 8 --- Conclusions --- p.72Chapter Appendix A --- Fractional Stochastic Integral for Deterministic Integrand --- p.75Chapter A.1 --- Mapping from Inner-Product Space to a Set of Random Variables --- p.76Chapter A.2 --- Fractional Calculus --- p.77Chapter A.3 --- Spaces for Deterministic Functions --- p.79Chapter Appendix B --- Three Approaches of Stochastic Integration --- p.82Chapter B.1 --- S-Transformation Approach --- p.84Chapter B.2 --- Relationship between Three Types of Stochastic Integral --- p.89Reference --- p.9

Stochastic modelling of long-term persistence in streamflow sequences

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