報告題目💆🏼：A hybrid Monte Carlo acceleration method of pricing basket options based on splitting
中文標題🕧：基於分割的組合蒙特卡羅加速定價方法
報告時間：2019年4月7日10:30-11:30
報告地點：必一体育平台二樓會議室
報告人：徐承龍教授
報告摘要：Pricing basket options has always been one of the key problems in financial engineering because of high dimensionality and low convergence rate. This paper proposes a hybrid Monte Carlo variance reduction method for pricing basket options. First, by splitting the payoff of the basket option into two parts, we can price basket options by value the two parts respectively. The first part has a closed-form expectation formula, the second part can be considered as a small probability event. To reduce variance for simulating the second part, the conditional Monte Carlo (CMC) method combined with the importance sampling(IS) method is adapted. Because these two methods are all effective to deal with small probability events. For IS method, it is a challenge to compute the optimal parameters with as little computational cost as possible. Therefore, an efficient prediction–correction(PC) iteration algorithm based on moment estimation is proposed to determine the optimal parameters in the importance sampling method. Some theoretical analyses for the existence and uniqueness of the optimal parameters in the IS method and the convergence of the PC method are also given. Numerical results show that the hybrid variance reduction method has great variance reduction effect and PC iteration algorithm can save a lot of computing costs comparing with the traditional Newton’s iteration method.