Hawkes跳扩散模型下的脆弱期权定价  

Vulnerable option pricing under the Hawkes jump-diffusion model

作　　者：马勇[1] 吕建平 Ma Yong;Lü Jianping(College of Finance and Statistics,Hunan University,Changsha 410079,China)

机构地区：[1]湖南大学金融与统计学院,湖南长沙410079

出　　处：《系统工程学报》2022年第5期605-616,共12页Journal of Systems Engineering

基　　金：国家自然科学基金资助项目(71971077);湖南省优秀青年科学基金资助项目(2019JJ30001).

摘　　要：研究了随机利率下含交易对手风险的期权定价问题.假设具有随机波动率的标的资产价格与交易对手资产价值是随机相关的,且假设它们的跳跃都服从具有自刺激性的Hawkes过程.针对所构建的期权定价模型,求得了脆弱欧式期权价格的半解析表达式.数值分析中,通过快速傅里叶变换方法计算期权价格,发现所构建模型的期权价格要高于Poisson跳模型、固定相关模型和固定利率模型.此外,期权价值随违约边界值和破产成本比例的增大而减小;期权价值随标的初始价格和交易对手资产初始价值的增大而增大.This paper investigates the issue of option pricing with counterparty risk under stochastic interest rate.Assume that the value of the underlying asset with stochastic volatility and the value of the counterparty asset are randomly correlated,and assume that their jumps are driven by the self-exciting Hawkes processes.The semi-analytical expression for the vulnerable European option price under the proposed model is obtained.In the numerical analysis,the option price is calculated by the fast Fourier transform method,and find the option price under the constructed model is higher than the Poisson jump model,the constant correlation model and the constant interest rate model.Moreover,option price decreases with the default boundary and the bankruptcy cost ratio;option price increases with the underlying initial price and the counterparty asset initial value.

关 键 词：期权定价 Hawkes过程 随机相关 随机利率 

分 类 号：F830[经济管理—金融学]