Calculation of Options Using Stochastic Volatility Models Based on Exact Simulation

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.

Key words:stochastic volatility; exact simulation; acceleration; conditional Monte Carlo; Greeks