混合指数跳扩散模型下基于FST方法的期权定价  

Option Pricing Under Mixed Exponential Jump Diffusion Model Based on the FST Method

作　　者：张素梅 赵洁琼 ZHANG Su-mei;ZHAO Jie-qiong(School of Sciences,Xi'an University of Post and Telecommunications,Xi'an 710121)

机构地区：[1]西安邮电大学理学院,西安710121

出　　处：《工程数学学报》2020年第2期165-176,共12页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11601420);陕西省自然科学基金(2017JM1021);陕西省教育厅科学计划项目(17JK0714).

摘　　要：混合指数跳扩散模型因其能够近似任意分布被广泛应用于刻画股价实际变动趋势.本文利用傅里叶空间时间步长(Fourier Space Time-stepping,FST)方法研究混合指数跳扩散模型下的欧式期权定价.通过傅里叶变换和特征指数将模型所满足的偏积分-微分方程转换为常微分方程并求解,得到了欧式期权价格.数值结果表明FST方法精度高、运行时间短.然后,通过搜集市场交易数据,利用非线性最小二乘方法,将得到的期权价格应用于模型校正,得到符合实际市场的模型参数.通过检验跳参数对隐含波动率图像的影响,发现混合指数跳扩散模型能够很好地体现资产收益的“波动率微笑”等特征.The mixed exponential jump-diffusion model that can approximate any distribution is widely used to describe the actual trend of stock price.Based on the Fourier Space Time-stepping(FST)method,this paper considers European option pricing under the mixed exponential jump-diffusion model.By the Fourier transform and the characteristic exponent,the partial integral-differential equation for pricing European options is transformed into an ordinary differential equations and solved to obtain European option prices.Numerical results indicate that the FST method is accurate and fast.Moreover,by collecting real market data and the nonlinear least squares method,we apply the obtained option price to model calibration to obtain the model parameters which match the real market.By examining the impact of jump parameters on the implied volatility,we find that the mixed exponential jump-diffusion model can well reflect the volatility“smile”of asset returns.

关 键 词：混合指数跳扩散模型 FST方法 欧式期权定价 偏积分-微分方程 模型校正 

分 类 号：O175.2[理学—数学] F830.9[理学—基础数学]