Pricing Of Option Under Fractional Brownian Motion And Stochastic Rate

Option pricing is one of the important elements of financial mathematics and econometrics, and its research and development are far-reaching impact on finance and capital markets.In recent years, with the exception of well-known European options and American options, a large number of new financial derivatives are derived in the international financial derivative markets. Among them, the power options and reset options are two new and more typical options.This dissertation studies the power options and reset option, and obtains the following results:①Pricing of Eurpean power options under fractional Ornstein-Uhlenback(O-U)process and stochastic rateConsidering the randomness and mean-reversion of interest rate and underlying asset, we incorporate an expanding Vasick model and fractional O-U process to study the pricing of European power options. Pricing formulas of two kinds of European power options were obtained under the hypothesis that the underlying asset and interest rate obey to fractional O-U process and expanding Vasick model, respectively. Besides, the Put-Call parity for European power options was presented.②Pricing of reset option under fractional jump-diffusions process and stochastic rateUnder the assumptions that the exchange rate and the price of underlying asset obey an expanding Vasick model and a fractional jump-diffusions process respectively, we obtained the pricing formulas of European call option and the reset option with predetermined dates by means of the no-arbitrage theory and multivariable normal distribution.