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                                                     Seminar

             Department of Systems Engineering and Engineering Management
                                  The Chinese University of Hong Kong

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Title

:

Jump Diffusion Processes in Financial Modeling

　

　

　

Speaker

:

Ning Cai

　

　

Department of Industrial Engineering and Operations Research

　

　

Columbia University

　

　

　

Date

:

March 7th, 2008 (Friday)

　

　

　

Time

:

11:30 a.m. -12:30 p.m.

　

　

　

Venue

:

Room 513

　

　

William M.W. Mong Engineering Building

　

　

(Engineering Building Complex Phase 2)

　

　

CUHK

　

　

　

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Abstract:
　

The talk includes two parts. The first part is about a hyper-exponential jump diffusion model for option pricing. The main objective is to extend the analytical tractability of the Black-Scholes model to alternative models with jumps, no matter whether the jump sizes have exponential-type tails or power-type tails. More precisely, we study a jump diffusion model for asset prices whose jump sizes are hyper-exponentially distributed. The hyper-exponential distribution can approximate most heavy-tail distributions as closely as possible, including both power- and exponential-type distributions. We demonstrate the hyper-exponential jump diffusion model can lead to analytical solutions for popular path-dependent options such as lookback, barrier, quantile, and perpetual American options. Numerical examples indicate that the formulae are easy to implement and accurate. These analytical solutions are made possible mainly because we solve several high-order integro-differential equations explicitly related to first passage time problems and optimal stopping problems.

In the second part, we propose a two-factor equilibrium model for electricity spot and futures prices. Not only does our model capture features such as spikes and seasonality, but it also has some other properties. First, it can incorporate oligopoly. Second, the spot prices have infinite expectations, but the futures prices have finite expectations.


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Biography:
　

Ning Cai is currently a Ph.D. candidate in financial engineering in the Department of Industrial Engineering and Operations Research at Columbia University. He received a M.S. in operations research at Columbia University in 2005 and both B.S. and M.S. in probability and statistics at Peking University.

Ning Cai\'s research interests include financial engineering and applied probability. More precisely, his research focuses on modeling of general financial markets as well as electricity markets and asset pricing under jump diffusion models. In addition, his research also encompasses Asian option pricing and Laplace transform inversion algorithm. In November 2007, he won the Second Place of the Best Student Research Paper Award in Financial Services Section in INFORMS for his paper coauthored by Steven Kou, entitled \"Option Pricing Under a Hyper-Exponential Jump Diffusion Model\".


************************* ALL ARE WELCOME ************************

　

　

　

Host

:

Prof. Chen Nan

Tel

:

(852) 2609-8237

Email

:

nchen@se.cuhk.edu.hk

　

　

　

Enquiries

:

Prof. Nan Chen or Prof. Sean X. Zhou

　

:

Department of Systems Engineering and Engineering Management

　

　

CUHK

Website

:

http://www.se.cuhk.edu.hk/~seg5810

Email

:

seg5810@se.cuhk.edu.hk

　

　

　

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