Research On Two Problems Of European Option Pricing

In this paper we consider two problems on European option pricing: pricing option on underlying assets driven by geometric fractional brownian motion, martingale methods on option pricing when volatility is stochastic process.Firstly, Without any market assumptions, Mogens Bladt and Tina Haviid Rydberg use merely probability measure of price process and actuarial consideration for pricing options. Based on their work, this paper obtains European option pricing formula when underlying assets are driven by g geometric fractional Brownian motion, and point out geometric Brownian motion is a special case of our model. Besides, we compare to the Greece letters of traditional B-S formula, and we find that when H= 12 ,the Greece letters of traditional B-S formula and fractional B-S formula are the same, the call and put have the same parity relations. We apply fractional B-S formula with valuing of strategic invest projects, we can make more scientific and rational value.Secondly, in the third part , we consider the improving problem about the volatility of Black-Scholes model .we major in modeling volatility and pricing these models. In the end , we study famous Hull and White model of the volatility of underlying assets are stochastic process, use equivalent martingale methods ,obtained the analytic solution of European option pricing, extend B-S model.