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随机波动率模型下基于精确模拟算法的期权计算理论
引用本文: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.
作者姓名:马俊美  杨宇婷  顾桂定  徐承龙
作者单位:上海财经大学 数学学院, 上海 200433; 应用数学福建省高校重点实验室(莆田学院), 福建 莆田 351100;上海市金融信息技术研究重点实验室,上海 200433,上海财经大学 数学学院, 上海 200433,上海财经大学 数学学院, 上海 200433,上海财经大学 数学学院, 上海 200433
基金项目:国家自然科学基金(No.11271243和No.11271240);上海优秀青年基金(No.ZZCD12007).
摘    要:基于两类随机波动率模型研究了欧式期权的价格和敏感性估计问题.在Broadie和Kaya的精确模拟算法基础上,讨论了舍取抽样技术在精确模拟算法中的有效应用.在此基础上研究条件蒙特卡罗、对偶变量技术等方差减小技术在欧式期权定价和敏感性Greeks计算中的加速问题.数值结果表明,相比欧拉离散和原始的蒙特卡罗模拟算法,基于精确模拟算法的条件蒙特卡罗加速技术能得到无偏且方差更小的估计值,具有较好的误差减小效果.该算法可以很方便地解决其他更加复杂的金融产品的计算问题,如障碍期权的定价和敏感性估计问题、篮子期权的计算问题等.

关 键 词:随机波动率  精确模拟  加速  条件蒙特卡罗  Greeks
收稿时间:2017/2/21 0:00:00
修稿时间:2017/5/17 0:00:00

Calculation of Options Using Stochastic Volatility Models Based on Exact Simulation
MA Junmei,YANG Yuting,GU Guiding and XU Chenglong.Calculation of Options Using Stochastic Volatility Models Based on Exact Simulation[J].Journal of Tongji University(Natural Science),2017,45(10):1539-1548.
Authors:MA Junmei  YANG Yuting  GU Guiding and XU Chenglong
Institution:Mathematical School, Shanghai University of Finance and Economics, Shanghai 200433, China; Key Laboratory of Applied Mathematics (Putian University), Fujian Province University, Putian 351100, China; Shanghai Key Laboratory of Financial Information Technology, Shanghai 200433, China,Mathematical School, Shanghai University of Finance and Economics, Shanghai 200433, China,Mathematical School, Shanghai University of Finance and Economics, Shanghai 200433, China and Mathematical School, Shanghai University of Finance and Economics, Shanghai 200433, China
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.
Keywords:stochastic volatility  exact simulation  acceleration  conditional Monte Carlo  Greeks
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