Smart Monte Carlo: various tricks using Malliavin calculus
介绍如何用Malliavin微积分平滑收益函数，解决蒙特卡洛模拟中希腊字母计算耗时且收敛慢的问题，并通过数值结果展示其效率及适用条件。
Abstract Current Monte Carlo pricing engines may face a computational challenge for the Greeks, not only because of their time consumption but also their poor convergence when using a finite difference estimate with a brute force perturbation. The same story may apply to conditional expectation. In this short paper, following Fournié et al (Fournié E, Lasry J M, Lebuchoux J, Lions P L and Touzi N 1999 Finance Stochastics 3 391-412), we explain how to tackle this issue using Malliavin calculus to smoothen the payoff to estimate. We discuss the relationship with the likelihood ratio method of Broadie and Glasserman (Broadie M and Glasserman P 1996 Manag. Sci. 42 269-85). We show by numerical results the efficiency of this method and discuss when it is appropriate or not to use it. We see how to apply this method to the Heston model.