带跳的Heston-CIR混合模型下的欧式期权定价  

European Option Pricing under the Hybrid Heston-CIR Model with Jumps

作　　者：白亚楠 汪育兵 BAI Ya-nan;WANG Yu-bing(Institute of Statistics,Lanzhou University of Finance and Economics,Lanzhou 730101,China)

机构地区：[1]兰州财经大学统计学院,甘肃兰州730101

出　　处：《兰州文理学院学报（自然科学版）》2020年第3期18-23,87,共7页Journal of Lanzhou University of Arts and Science(Natural Sciences)

摘　　要：经典的Heston模型中波动率虽然满足随机性,但该模型没有考虑到随机利率和突发事件对金融产品价格的影响.鉴于此建立带跳的混合随机波动率与随机利率下的欧式期权定价模型.首先,假定标的资产为带跳的Heston-CIR混合模型,并通过测度变换将其变换到远期测度下.其次,利用快速傅里叶变换法解得期权价格.最后进行数值模拟,结果表明:带跳的Heston-CIR模型下的标的资产路径变化比Heston-CIR混合模型下的更符合金融实际.It was showed in empirical studies that although the classical Heston model had the characteristics of mean reversion,the influence of random interest rate and unexpected events on the price of financial products was not taken into account.On this condition,the European option pricing model under the mixed stochastic volatility and interest rate with jumps was established.Firstly,it was assumed that the underlying asset obeyed the hybrid Heston-CIR model with jumps and transformed to the forward measure by measure transformation.Secondly,the Fast Fourier Transform(FFT)method was used to solve the approximate solution of the option price.Finally,it was showed by the numerical simulation results that the change of the underlying asset path under the Heston-CIR model with jump was more consistent with the financial reality than under the hybrid Heston-CIR model.

关 键 词：Heston模型 CIR随机利率模型 跳过程 快速傅里叶变换(FFT) 

分 类 号：F830.59[经济管理—金融学]