A smooth estimator for MC/QMC methods in finance

We investigate the effect of martingale control as a smoother for MC/QMC methods. Numerical results of estimating low-biased solutions of the American put option price under the Black-Scholes model demonstrate the unreliability of using QMC methods. But it can be fixed by considering a martingale control variate estimator. In another example of estimating European option prices under stochastic volatility models, randomized QMC methods improve the variance by a single digit. After adding a martingale control the variance reduction rations raise up to 700 times for randomized QMC and about 50 times for MC simulations. An analysis to exploit the effect of the smoother is provided.