基于混合分数布朗运动环境的Black-Scholes模型新解法

New Solution of Black-Scholes Model Under Mixed Fractional Brownian Motion

文章研究不具有平稳增量的随机过程下的欧式期权定价问题.假设标的资产价格变化过程由混合分数布朗运动来刻画,在此环境下研究欧式看涨期权.利用复制策略得到欧式看涨期权价值所满足的偏微分方程.结合欧式看涨期权价值满足的终端条件,运用Mellin变换得到偏微分方程的解析解,即混合分数布朗运动环境下欧式看涨期权定价公式.

European option pricing is studied under stochastic process with no stationary increment.Assuming that the underlying asset price change process is described by mixed fractional Brownian motion, we start the study of European call option. Replication strategies are used to get the part/a/differentia/equation of the Eu- ropean call option value. Combined with European call option value of terminal conditions, we use Mellin transform to derive the analytic solution of the partial differential equation. The pricing formula of European call option is obtained under mixed fractional Rrnwni ~