时间：2019年11月12日(周二)上午9:30-10:30
地点：中山北路校区理科大楼A1514会议室
题目：Hermite Expansion for Transition Densities of Irreducible Diffusions with An Application to Option Pricing
报告人：万相伟 副教授 上海交通大学安泰经济与管理学院
摘要：
A diffusion is said to be reducible if there exists a one-to-one transformation of the diffusion into a new one whose diffusion matrix is the identity matrix, otherwise it is irreducible. Most multivariate diffusions such as the stochastic volatility models are irreducible. As pointed out by Ait-Sahalia (2008), the straight Hermite expansion of Ait-Sahalia (2002) will not in general converge for irreducible diffusions. In this paper we manage to develop the Hermite expansion for transition densities of irreducible diffusions, which converges as the time interval shrinks to zero. By introducing a quasi-Lamperti transform unitizing the process' diffusion matrix at the initial time, we can expand the transition density of the transformed process using Hermite polynomials as the orthogonal basis. Then we derive explicit recursive formulas for the expansion coefficients using the Ito-Taylor expansion method, and prove the small-time convergence of the expansion. Moreover, we show that the derived Hermite expansion unifies some existing methods including the expansions of Li (2013) and Yang, Chen and Wan (2019). In addition, we demonstrate the advantage of Hermite expansion by deriving explicit recursive expansion formulas for European option prices under irreducible diffusions. Numerical experiments illustrate the accuracy and effectiveness of our approach. This is a joint work with Nian Yang from Nanjing University.
报告人简介：
万相伟博士，现为上海交通大学安泰经济与管理学院金融学长聘副教授。研究兴趣主要集中在金融工程、金融计量和金融经济学。相关成果发表于Journal of Econometrics, Mathematical Finance, Mathematics of Operations Research, Journal of Economic Dynamics and Control, Quantitative Finance等国际顶级刊物。