Application Of Fair Premium And Fuzzy Mathematics In Option Pricing

In this paper we consider three problems on European option pricing.Firstly, Using an actuarial approach, we deal with pricing formula of European option On Quanto option, and obtain pricing of European call and put option and put-call parity. `Secondly, using physical probabilistic measure of price process and the principle of fair premium, we generalize the results of Mogens bladt and Hviid Rydberg on European option pricing. Under the assumptions that stocks price process driven by fractional Brownian Motion and nonhomogeneous Poisson jump process, and the expected rateμ(t) and riskless rate r (t) are function of time , we obtain the accurate pricing formula and put-call parity of European option.Finally, the application of fuzzy sets theory to the Black-Scholes formula with dividends is proposed in this paper, the fuzzy pattern of Black-Schloes formula with dividends and put-call parity relationship are proposed. Under the considerations of fuzzy interest rate, fuzzy volatility, fuzzy stock price and fuzzy-valued function integral, the European option price will turn into be a fuzzy number. Thus we can get a computational method of belief degree.