Sean Han (Taiwan)

Abstract:

Under stochastic volatility models, we propose a new and generic control variates method to efficiently evaluate financial derivatives by means of Monte Carlo simulation. These controls are local martingales and are closely related to some imperfect hedging strategies. Therefore, reduced variances obtained from these Monte Carlo methods are not only measurements of computing efficiency but also represent risks associated to some particular trading strategy in the incomplete market. An asymptotic result is obtained to characterize the variance for rescaled stochastic volatility models. The analysis is done through a combination of perturbation techniques and an averaging effect. Several numerical examples, including some lower and upper American option prices, computed by Monte Carlo and/or Quasi-Monte Carlo methods are presented.