Exact Simulation Of Stochastic Volatility Models Using Quasi-monte Carlo Method

Traditional option pricing theory is based on Black-Scholes model, which is un-able to interpret important phenomena such as volatility smile and volatility surface.For this reason, more advanced models such as Stochastic Volatility Model (SV) andStochastic Volatility Model with Jumps (SVJ) are attracting more and more attentionrecently. Closed-form solution is very unlikely to exist for SV models, and the di-mension of the problem is often very high, making conventional numerical methodsunsuitable. Monte Carlo method (MC) is usually employed under this circumstance.This paper focuses on the improved method of solving option pricing problem underHeston stochastic volatility model. The solution error of MC method comes from dis-cretization error and variance. This paper applies Exact Simulation method and Quasi-Monte Carlo method to reduce error from these two aspects. Numerical results showthat exact simulation method eliminate discretization error and QMC method efective-ly accelerate the convergence of variance when dimension is low. Further more, QMCmethod combining with bridge sampling could significantly reduce variance when di-mension is high. Finally, this paper verifies that these techniques could be applied tomore complicated models such as SVJ model and achieve good results.