随机利率与非仿射跳扩散模型下的欧式期权定价  

European Option Pricing under Stochastic Interest Rate and Non-affine Jump Diffusion Model

作　　者：杜慧源 范小明[1] 李奥 DU Hui-yuan;FAN Xiao-ming;LI Ao(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《兰州文理学院学报(自然科学版)》2025年第1期22-28,共7页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：国家自然科学基金项目(P113123G02004)。

摘　　要：研究了具有随机利率和泊松跳的非仿射随机波动率模型下的欧式期权定价问题.首先,运用扰动法去逼近标的对数资产价格的特征函数,并得到近似的解析式;然后,运用快速Fourier变换等方法推导出欧式期权的定价公式;其次,运用数值计算比较随机利率、固定利率以及非仿射波动率过程分别对欧式看涨期权价格的不同作用,以及分析模型中利率的波动率参数和仿射结构参数对期权价格的影响.结果表明,二者对期权价格结果的影响均是正向的,且非仿射随机波动率模型比仿射随机波动率模型具有更高的灵活性.This paper studies the pricing problem of European options under non-affine stochastic volatility model with random interest rate and Poisson jump.First,perturbation method is used to approximate the characteristic function of the underlying logarithmic asset price,and the approximate analytic formula is obtained.Then,the pricing formula of European option is derived by using fast Fourier transform.Secondly,the numerical calculation is uesd to compare the different effects of stochastic interest rate,fixed interest rate and non-affine volatility on the price of European call options,and analyze the effects of interest rate volatility parameters and affine structure parameters on the price of option.The results show that both of them have positive effects on option price,and the non-affine stochastic volatility model is more flexible than the affine stochastic volatility model.

关 键 词：非仿射 随机波动率 期权定价 快速FOURIER变换 扰动法 

分 类 号：O212.1[理学—概率论与数理统计]