学术报告 报告题目一：Sensitivity Analysis for American Options
报 告 人：刘彦初 教授 （中山大学岭南(大学)学院）
报告时间：2016年5月27日（周五）下午 15:00-16:00
报告题目二：Discrete Sum of Geometric Brownian Motions and Asian Options
报 告 人：朱凌炯 教授 (佛罗里达州立大学)
报告时间：2016年5月27日（周五）下午 16:10-17:10
报告地点：4号楼4141室
欢迎广大师生前往！
数学学院
2016年05月25日
报告一摘要：
In this paper, we develop efficient Monte Carlo methods for estimating American option sensitivities. The problem can be reformulated as how to perform sensitivity analysis for a stochastic optimization problem with model uncertainty. We introduce a generalized infinitesimal perturbation analysis (IPA) approach to resolve the difficulty caused by discontinuity of the optimal decision with respect to the underlying parameter. The IPA estimators are unbiased if the optimal decisions are explicitly known. To quantify the estimation bias caused by intractable exercising policies in the case of pricing American options, we also provide an approximation guarantee that relates the sensitivity under the optimal exercise policy to that computed under a sub-optimal policy. The price-sensitivity estimators yielded from this approach demonstrate significant advantages numerically in both high-dimensional environments and various process settings. We can easily embed them into many of the most popular pricing algorithms without extra simulation effort to obtain sensitivities as a by-product of the option price. Our generalized approach also casts new insights on how to perform sensitivity analysis using IPA: we do not need path-wise continuity to apply it. (This paper has been published on Operations Research and it is a joint work with Prof. Nan Chen from Chinese University of Hong Kong.)
报告人简介：
刘彦初，男，四川眉山人。现就职于中山大学岭南（大学）学院，担任金融学助理教授。香港中文大学金融工程博士，中国科学技术大学理学硕士与理学学士。持有金融风险管理师（Financial Risk Manager, 简称FRM）证书。主要研究兴趣为金融经济学以及金融工程中的计算方法与相关应用。已发表SSCI/SCI/EI收录论文5篇。目前主持国家自然科学基金青年项目一项，以及中央高校基本科研业务费项目一项。
报告二摘要:
The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in finance. We consider the asymptotics of the discrete time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps. We derive the asymptotics for the price of Asian options in the Black-Scholes model and numerically test our results and compare with the existing results in the literature. This is based on the joint work with Dan Pirjol.