An efficient conditional Monte Carlo method for European option pricing with stochastic volatility and stochastic interest rate

This paper studies the variance reduction methods for pricing European options under stochastic volatility and stochastic interest rate model. A general conditional Monte Carlo pricing framework is constructed to reduce the variance and save the time cost of Monte Carlo simulation. Based on Martingale Representation Theorem, two efficient martingale control variates are designed to combine with the conditional Monte Carlo simulation. Numerical results show that this hybrid method has great variance reduction effect and robust performance. The idea is also applicable for pricing other financial derivatives with stochastic volatility and/or stochastic interest rate.