次分数随机利率模型下欧式期权定价的Mellin变换法

Mellin Transform Method for European Option Pricing Under Sub-fractional Stochastic Interest Rate Model

给出了金融市场的即期利率由次分数Vasicek随机利率模型驱动时的欧式看涨期权定价公式.利用Mellin变换方法求解该模型下欧式期权价值满足的Black-Scholes偏微分方程,得到了欧式看涨期权简单积分形式的定价公式,并通过Mellin变换的卷积公式得到了欧式看涨期权的解析解.数值算例验证了Mellin变换法的收敛性,并分析了各种参数对欧式看涨期权价值的影响,从而推广了期权定价的方法.

The pricing formula of European call option in financial market is given when the spot interest rate is driven by sub-fractional Vasicek stochastic interest rate model.The Mellin transform method is used to solve the Black-Scholes partial differential equation satisfied by European option value,and get the pricing formula in simple integral form of European call option.The analytical solution of European call option is obtained through the convolution formula of Mellin transform.A numerical example verifies the convergence of Mellin transform technology,and analyzes the influence of various parameters on the value of European call options,thus promoting the option pricing method.