| In 1973, two great financial theoristes and practicers Fisher Black and Myron Sc-holes published their famous paper " The Pricing of Options and Corporate Liability " which gave the the Black-Scholes formula, an explicit formula of the pricing of European Option. This is a breakthrough of modern Mathematical Finance. From then on, the research of modern Mathematical Finance gained rapid development with tremendous achievements. Most remarkeable of all, the Black-Scholes model has not only been ob-tained plentiful results in theoretical rasearch,but also been applied in financial market broadly.In this dissertation, on the basis of the stochastic integral theory of the fractional Brownian Motion and the study of option pricing in the fractional Black-Scholes Model, we studied fractional Black-Scholes Model of mathematical finance with arbitrary Hurst parameter are studied.In introduction, we introduced the main research content, results and hot topics of option pricing theory,the research actuality of option pricing theory in the the fractional Black-Scholes Model and the main content of this paper.In chapter two, we introduced the fractional Black-Scholes Model and the formula of European option by using the conditional probability debsity.In Chapter three, we introduced several common Exotic options, we obtained the pricing formulas of Capped Call, Deductible Call, Payoff segment Call,Bi-direction Eu-ropean Option, binomial option and Convertible Band at arbitrary time before maturity.In Chapter four, we studied Multi-dimensional Fractional Black-Scholes model. In single asset and multi-noise, multi-asset and single noise, we obtained the picing formula of European contigent claim at arbitrary time before maturity.we obtained the pricing formulas of Bivariate Cash-or-nothing Call,C-Brick option,A Bivariate Asset-or-Nothing Call, A-Brick option. A natural conclusion is drawn and further research directions are given in the last chapter. |
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