主 题: Constructing Markovian Jump Processes Using Random Time Change: Theory, Financial Models and Option Pricing
报告人: Prof. Lingfei Li (The Chinese University of Hong Kong)
时 间: 2016-03-21 15:30-17:00
地 点: 理科1号楼 1479(北京大学数量经济与数理金融教育部重点实验室学术报告)
Markovian jump processes play an essential role in financial modelling and a useful approach for constructing them is random time change. In a time change framework, the modeler specifies the background process X (which is a Markov process), and the random clock T to construct a new Markov process X_T with jumps and other desirable features. Typically X and T are assumed to be independent to have tractability. This talk consists of two parts. In the first part, I will first review a classical time change technique called Bochner’s subordination, which corresponds to specifying T to be a Levy subordinator. Many popular financial models are constructed using this technique. However, Bochner’s subordination is limited in that the time-changed process X_T is time homogenous, which may fail to capture important empirical features such as fitting the volatility surface. As an improvement, we propose to specify T to be an additive subordinator to construct time-inhomogeneous Markovian jump processes, and this new time change technique is called additive subordination. We develop the theory of additive subordination and give Markov and semimartingale characterization of X_T. Examples will be provided to illustrate the application of additive subordination in financial modelling. In the second part of the talk, I will discuss analytical and computational methods for option pricing in models based on both Bochner’s subordination and additive subordination. Calibration results will be provided to show the excellent empirical performance of models constructed from additive subordination. 报告人简介： Dr. Lingfei Li received his B.S. in Applied Mathematics from Peking University, China in 2007, and his M.S. and Ph.D. in Industrial Engineering and Management Sciences from Northwestern University, USA in 2008 and 2012. He joined the Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong in June 2012. His research interests include financial engineering, mathematical finance and computational finance, and he has published in leading academic journals in his field, such as Finance and Stochastics, Mathematical Finance and Operations Research.
