基于无穷跳-扩散双因子交叉回馈模型的期权定价  

Option valuation for the double-factor-cross-feedback infinite activity jump-diffusion model

作　　者：朱福敏[1] 郑尊信[1] 吴恒煜[2,3] Zhu Fumin Zheng Zunxin Wu Hengyu(College of Economics, Shenzhen University, Shenzhen 518060, China Management School, Jinan University, Guangzhou 510000, China Collaborative Innovation Center of Financial Security, Chengdu 6100130, China)

机构地区：[1]深圳大学经济学院,广东深圳518060 [2]暨南大学管理学院,广东广州510000 [3]金融安全协同创新中心,四川成都610000

出　　处：《系统工程学报》2017年第5期638-647,共10页Journal of Systems Engineering

基　　金：国家自然科学基金资助项目(71601125;71471119;71171168);教育部人文社会科学研究青年基金资助项目(16YJC790030)

摘　　要：为研究股市无穷跳跃和连续扩散行为特征,提出了一类能够捕捉无穷跳和扩散之间交互影响的动态跳-扩散双因子交叉回馈模型.借助Lévy过程条件特征函数、局部风险中性关系和贝叶斯学习技术,给出了动态跳-扩散随机过程的期权定价方法,并进行标准普尔500指数欧式期权标准化合约的实证研究,对比了有限跳-扩散及无穷跳-扩散模型定价差异.研究结果表明:以VG为基础的无穷跳-扩散全面优于Merton的有限跳-扩散双因子模型;跳-扩散交又回馈模型具有最小的期权定价误差;跳跃行为相比扩散波动具有更高的持续性、更强的杠杆作用和更高的风险市场价格.In order to study the behaviors of infinite jumps and diffusions in stock markets, this paper presents a dynamic double-factor-cross-feedback jump-diffusion process that captures the interaction between jumps and diffusions. Using the conditional characteristic function of Levy process, local risk-neutral valuation re- lationship and sequential Bayesian learning technology, this paper develops a generalized risk-neutral pricing method for the dynamic jump-diffusion model, empirically studies the standardized European options on S＆P 500 index, and gives a comprehensive comparison of the pricing accuracy between the finite activity jump- diffusion model and infinite activity jump-diffusion model. Compared with the diffusion volatility, the infinite activity jump-diffusion model （VG-JD） performs better than the finite jump-diffusion model （MJ-JD）. The cross-feedback model always performs the best with the lowest errors in option valuation. It also finds that, the jumps have a higher persistence, stronger leverage effect and a higher market price.

关 键 词：跳-扩散模型 无穷跳跃行为 交叉回馈 序贯Baycs学习 

分 类 号：F830.9[经济管理—金融学]