数学科学系

Department of Mathematical Sciences

A New Approach for Computing Greeks in Diffusion Models

报告人:梁超, 美国 Tilden Park Capital Management

报告时间:20181025 (周四) 下午4:105:10

地点: 数学系理科楼A404

摘要: The European option is a kind of financial derivatives, and its risk management is of essential importance for both market players and regulators (especially after the 2008 financial crisis).  I will introduce the commutator method to compute the Greeks (risk numbers) for the European option.

The Black-Scholes model and its local and stochastic volatility extensions will be introduced.  The extended models are more realistic but mathematically more challenging. To be explicit, the Partial Differential Equations (PDEs) from these models do not allow analytical solutions in general. The partial differential operators under the extended models can be viewed as the Black-Scholes PDE operator plus a perturbation operator. These two operators do not commute in general. Based on my thesis advisors work on computing the remaining terms when commuting two operators, I developed a method to compute the Greeks under such extended models.

In the last part of the talk, I will show how to apply this new method to the Constant Elasticity of Variance (CEV) model. Possible future research directions will also be discussed.

报告人简介: 梁超, 我系2003级本科生,2009年在我系获得硕士学位后,于2014在美国宾州州立大学数学系获得博士学位, 2014-2016就职于摩根士丹利纽约总部,目前在Tilden Park Capital Management工作,主要研究随机微分方程、金融数学及应用(期权定价、风险控制等)。