分数布朗运动环境下欧式篮子期权定价

Pricing of European basket option in fractional Brownian motion environment

分数布朗运动具有的长程相关性和自相似性,因此用分数布朗运动来刻画资产价格的变化更符合金融市场价的实际情况.保险精算方法将期权定价问题转化为等价的公平保费确定问题,对任何市场均有效.假定股票价格服从分数布朗运动驱动的随机微分方程,且期望收益率、无风险利率、波动率均为常数,利用分数布朗运动随机分析理论和保险精算方法,推导出了欧式几何篮子期权定价公式.且当指数H=1/2时,结论为标准布朗运动下的欧式篮子期权定价公式.

Fractional Brownian motion which had self-similarity and long-range correlation,so it was better for financial market by Fractional Brownian motion to describe the changes of asset prices.Actuarial approach transformed option pricing problem into determination of the equivalent fair insurance premiums,it was effective for any market.This paper assumed that the stock price process satisfied the stochastic differential equation driven by the fractional Brownian motion,the expected of return,the risk free interest rate and the volatility are constant.The pricing formulae for geometric European basket option was obtained by using fractional Brownian motion stochastic analysis theory and the actuarial approach.The result was the formula of European basket option pricing under Brownian motion environment when H =1/2.