Pricing Accelerated Simulation Theory of Generalized Autoregressive Conditional Heteroskedasticity Model

Abstract:

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.

Key words:GARCH; stochastic volatility; accelerate; control variate; variance derivatives