一类特殊混合跳扩散Black-Scholes模型的欧式回望期权定价

Pricing European Lookback Option in a Special Kind of Mixed Jump-Diffusion Black-Scholes Model

在混合跳扩散Black-Scholes(B-S)模型下研究了欧式固定履约价的回望期权定价问题.结合Merton假设条件以及风险资产所满足的随机微分方程的Cauchy初值问题,利用多尺度参数摄动方法求解了欧式回望期权所适合的抛物型随机偏微分方程,给出了欧式固定履约价的回望期权的近似定价公式,并利用Feynman-Kac公式分析了近似公式的误差估计.数值模拟研究表明,当混合跳扩散模型的波动率为常数时,欧式回望期权是有精确解的,并且随着模拟阶数的增大,回望期权价格的近似解逐渐地逼近期权价格的精确解.

This article considers the pricing problem of European fixed strike lookback options under the environment of mixed jump-diffusion fractional Brownian motion.Under the con-ditions of Merton assumptions,we analyze the Cauchy initial problem of stochastic parabolic partial differential equations which the risky asset satisfied,by using the perturbation method of multiscale-parameter,the approximate pricing formulae of European lookback options are given by solving stochastic parabolic partial differential equations.Then the error estimates of the approximate solutions are given by using Feynman-Kac formula.Numerical simulation illustrate that the European lookback options have exact solutions when the volatilities are constant,and as the order of simulation increases,the approximate solutions are gradually approximates the exact solutions.