非仿射随机波动率跳扩散模型的利差期权定价

Valuation on Outer Performance Option in a Non-Affine Stochastic Volatility Jump-diffusion Model

在两标的资产价格满足一类随机利率、随机波动率及跳跃均存在于资产价格和波动率的非仿射跳扩散模型下考察了利差期权的定价.首先,利用泰勒公式将非线性微分方程线性化,得到了两标的资产对数价格的近似联合密度特征函数;然后,使用Fourier逆变换等方法,获得了利差期权定价理论的半封闭公式,并将其推广到价差期权的定价.最后,通过数值实验,表明非仿射随机波动率跳扩散的利差期权定价模型比仿射随机波动率模型具有更高的精确性,并且扩散波动和跳跃波动对期权价格影响显著.

The problem of outer performance option pricing when two underlying assets follow the non-affine jump-diffusion model in which stochastic interest rate,stochastic volatility and jumps in both two underlying assets and volatility are considered in this paper.Firstly,by using the Taylor formula to solve the nonlinear differential equation of linear problems,we obtain an approximate solution for characteristic function for the underlying log-asset price.Then,a semi-analytical pricing formula for the price of outer performance option is attained by means of Fourier inversion transform,we then apply the model to price performance option.Numerical examples show that the non-affine stochastic volatility jump-diffusion option pricing model a more accurate than the affine stochastic model,and the option price has significant effects by the volatilities in both diffusion and jumps.