Least-square-based control variate method for pricing options under general factor models

摘要

This paper proposes a class of simple but efficient control variate method for pricing derivatives under multiple factor models including stochastic volatility and stochastic interest rate model. The control variate can help us to obviously reduce the error of Monte Carlo simulation. Briefly speaking, we construct a virtual asset with deterministic volatility and deterministic interest rate which has high correlation with the original underlying asset based on the method of least square, and use derivative written on the virtual asset as control variate in pricing derivative written on the original underlying asset. Some theoretic results can help us to understand the mechanism of a control variate. Numerical examples show that simulation error is significantly reduced by our method. The advantage of our method is that it has no analytic form request for the underlying asset model, so the method is flexible to deal with and broadly applicable for derivative pricing.