广义自回归条件异方差模型加速模拟定价理论  

Pricing Accelerated Simulation Theory of Generalized Autoregressive Conditional Heteroskedasticity Model

作　　者：马俊美 卓金武 张建 陈渌 MA Junmei;ZHUO Jinwu;ZHANG Jian;CHEN Lu(School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China;Shanghai Key Laboratory of Financial Information Technology, Shanghai 200433, China;KeyLaboratory of Applied Mathematics, Fujian Province University(Putian University), Putian 351100, China;School of Information Management and Engineering, Shanghai University of Finance andEconomics, Shanghai 200433, China)

机构地区：[1]上海财经大学数学学院,上海200433 [2]上海市金融信息技术研究重点实验室,上海200433 [3]应用数学福建省高校重点实验室(莆田学院),福建莆田351100 [4]上海财经大学信息管理与工程学院,上海200433

出　　处：《同济大学学报（自然科学版）》2019年第3期435-443,共9页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金(11271243;11226252);上海优秀青年基金(ZZCD12007);应用数学福建省高校重点实验室(莆田学院)开放课题(SX201704)

摘　　要：研究了广义自回归条件异方差(GARCH)模型下方差衍生产品的加速模拟定价理论.基于Black-Scholes模型下的产品价格解析解以及对两类标的过程的矩分析,提出了一种GARCH模型下高效控制变量加速技术,并给出最优控制变量的选取方法.数值计算结果表明,提出的控制变量加速模拟方法可以有效地减小Monte Carlo模拟误差,提高计算效率.该算法可以方便地解决GARCH随机波动率模型下其他复杂产品的计算问题,如亚式期权、篮子期权、上封顶方差互换、Corridor方差互换以及Gamma方差互换等计算问题.The accelerated simulation pricing theory of variance derivatives under generalized auto regressive conditional heteroskedasticity(GARCH) stochastic volatility model was studied. Based on the analytical solution under the Black-Scholes model and their moments analysis of these two kinds of processes, a more efficient acceleration technique of control variate was proposed and the method of selecting optimal control variate was also given. The numerical results show that the proposed accelerated simulation method of control variate effectively reduce the simulation error and improve the computational efficiency. The algorithm can also be used to solve the computational problems of other complex products under GARCH stochastic volatility model, such as Asian option, Basket option, Capped variance swap, Corridor variance swap and Gamma variance swap, etc.

关 键 词：GARCH 随机波动率 加速 控制变量 方差衍生产品 

分 类 号：F830.9[经济管理—金融学] O211.5[理学—概率论与数理统计]