区制转换与Hawkes跳扩散模型下的脆弱欧式期权定价  

Vulnerable European option pricing in a regime-switching and Hawkes jump diffusion model

作　　者：杜慧源 范小明[1] DU Huiyuan;FAN Xiaoming(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,Sichuan,China)

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《山东大学学报(理学版)》2025年第3期22-32,共11页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12371178);西南交大创新项目(P113123G02004)。

摘　　要：研究随机波动率和随机利率模型下含交易对手违约风险的期权定价问题,该模型中波动率和利率过程的均值回复水平均由有限状态空间的连续马尔可夫过程控制,并假设标的资产价格过程和交易对手的资产价格过程均含有跳,且它们的跳均服从具有自刺激性的Hawkes过程,以及假设波动率过程中也含有跳。利用测度变换、求解贴现特征函数、多元傅里叶变换等方法,推导欧式脆弱期权的解析定价公式;然后利用快速傅里叶变换(fast Fourier transform,FFT)方法计算期权解析定价公式的有效逼近,并通过蒙特卡罗仿真检验逼近的准确性;最后,对所提模型中不同参数对脆弱看涨期权价格的敏感性进行分析,并通过数值实验对比所提出模型与不具有马尔可夫区制转换(Markov regime-switching,MRS)的随机利率模型的差异,说明在模型中引入区制转换对期权定价结果的影响。Option pricing with counterparty default risk under stochastic volatility and stochastic interest rate models is studied.In this model,the mean reversion levels of volatility and interest rate process are controlled by a continuous Markov process in a finite state space,and it is assumed that both the underlying asset price process and the counterparty asset price process contain jumps,and their jumps obey the Hawkes process with self-stimulation,and it is assumed that the volatility process also contains jumps.The analytical pricing formula of European vulnerable option is derived by means of measure transform,solution of discount characteristic function and multivariate Fourier transform.Then the fast Fourier transform method is used to calculate the effective approximation of the option analytic pricing formula,and the accuracy of the approximation is verified by Monte Carlo simulation.Finally,the sensitivity of different parameters in the proposed model to the price of vulnerable call options is analyzed,and the difference between the proposed model and the stochastic interest rate model without Markov regime-switching(MRS)is compared by numerical experiments,and the impact of the introduction of regime-switching in the model on the option pricing results is illustrated.

关 键 词：脆弱欧式期权 跳跃聚集 区制转换 快速傅里叶变换 

分 类 号：O211.6[理学—概率论与数理统计]