同济大学学报（自然科学版）2017，Vol.45Issue(10)：1539-1548,10.DOI:10.11908/j.issn.0253-374x.2017.10.017
随机波动率模型下基于精确模拟算法的期权计算理论
Calculation of Options Using Stochastic Volatility Models Based on Exact Simulation
摘要
Abstract
This paper researched the estimation of price and Greeks of European options on the two kinds of stochastic volatility models.Rejection sampling technique was discussed in detail to improve the sampling efficiency based on the exact simulation algorithm of stochastic volatility models of Broadie and Kaya.Then conditional Monte Carlo and antithetic variable techniques were used to reduce the variance of Monte Carlo simulation.The numerical results show that the combination of exact simulation and conditional Monte Carlo method can get unbiased estimation and smaller variance,compared with the crude Monte Carlo and Euler discretization.The algorithm proposed in this paper can also be used to solve the calculation problems of other more sophisticated products,such as the estimation of the price and Greeks for barrier options and basket options.关键词
随机波动率/精确模拟/加速/条件蒙特卡罗/GreeksKey words
stochastic volatility/exact simulation/acceleration/conditional Monte Carlo/Greeks分类
管理科学引用本文复制引用
马俊美,杨宇婷,顾桂定,徐承龙..随机波动率模型下基于精确模拟算法的期权计算理论[J].同济大学学报（自然科学版）,2017,45(10):1539-1548,10.基金项目
国家自然科学基金(11271243,11371105,11671246) （11271243,11371105,11671246）
上海市优秀青年基金(ZZCD12007) （ZZCD12007）
应用数学福建省高校重点实验室(莆田学院)开放课题(SX201704) （莆田学院）
