保险与金融工程教研室学术讲座

报告题目：Applications of the Dirac Delta Family Method in Implied Volatility, Risk-neutral Density, and High-dimensional Stochastic Control

报  告 人：崔振嵛（斯蒂文斯理工学院 副教授）

主  持 人：刘彦初（中山大学岭南学院 教授）

时      间：2023年12月29日（周五）14：30

地      址：岭南堂黄炳礼会议室(203)

语      言：中文+英文

讲座介绍:

In this talk, the Dirac Delta family method is introduced, which is based on orthogonal polynomial representations of the Dirac Delta function. We show how this method can lead to new valuation results in three financial applications. First, when combined with the change of variable technique, we obtain an explicit model-free formula for the Black-Scholes implied volatility. The formula is expressed through either a limit or as an infinite series of elementary functions, and we establish that the proposed formula converges to the true implied volatility value. Numerical and empirical examples illustrate the accurateness of the formula. Second, when combined with the celebrated Carr-Madan spanning formula, we derive a novel model-free representation of the risk-neutral density in terms of market-observed options prices. Compared to the widely used method for obtaining the risk-neutral densities via the Breeden–Litzenberger device, our method yields estimates of risk-neutral densities that are model-free, automatically smooth, and in closed-form. Third, when applied to calculating the conditional expectations arising from dynamical programming, we show that it leads to a novel numerical time-stepping approach for solving corresponding HJB system. We demonstrate the accuracy and efficiency of the method through solving some one-dimensional and two-dimensional control problems.

报告人介绍：

      崔振嵛，理学博士，Stevens Institute of Technology 商学院副教授，博士生导师， 博士毕业于University of Waterloo，现任International Journal of Finance and Economics 副主编。主要研究兴趣有金融工程，随机模拟，及金融科技，在 Econometric Theory, Mathematical Finance, INFORMS Journal on Computing, Journal of Financial Econometrics, European Journal of Operational Research， Annals of Operations Research 等杂志发表数十篇论文。目前主持 NSF CNS-2113906: “Fast Quantum Method for Financial Risk Measurement” 科研项目。

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      中山大学岭南学院共设八个教研室，以教研室作为人才培养的抓手，通过教研室之间交流、研讨和竞争，让教研室在课程建设、科研团队、党支部建设发挥三位一体的作用。教研室定期邀请嘉宾举办专题学术讲座，分享学术前沿资讯及教师学术研究方向和进展，促进学院师生之间、教研室之间的学术交流与合作。