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:

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.

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.