Wen Cheng's Homepage

Wen Cheng

Graduate Assistant

Department of Mathematics

Penn State University , University Park

Contact Information

Office: 009 McAllister Building
E-mail: cheng@math.psu.edu
office phone: (814)863-9672
webpage: http://www.math.psu.edu/cheng

Education

2003-2007, BS, Mathemetics, Nankai University
2007-present, PhD candidate, Applied Mathematics with minor in Computational Science and minor in Statistics, Penn State University

Research

Advisors: Victor Nistor AND Anna Mazzucato
Research Interest: Mathematical Finance (derivative pricing, term structure modeling, etc.), Financial Econometrics, Numerical PDE, PDE Analysis, Stochastic Process.

My current research is mainly on analytical approximations of the Green's function of various kinds of second order parabolic PDEs. For a parabolic Cauchy problem, in general we do not have analytic closed form solutions. As a result, one usually needs to use numerical methods (FEM, FDM, etc.). An alternative is to approximate the Green's function analytically, then the convolution of this approximated Green's function and the initial data is an approximation of the solution to the initial Cauchy problem. One of the important applications of our results is to price options. And for European options, closed form formulas have been obtained. Our results can also be applied to American options, model calibration, hedging and many other fields of finance. Very recently I am working on projects on computational finance and financial econometrics by using numerical and statistical methods. I am also trying to work on Stochastic PDEs and their applications in finance. The following is a list of projects that I am involved.

Preprints/In preparation

Mathematics

1. Approximate Solutions to Second Order Parabolic Equations II: time-dependent coefficients, with A. Mazzucato, AND V. Nistor, 47 pages, IMA preprint #2372, Jun. 2011. [PDF]

2. Approximate Solutions to Second Order Parabolic Equations III, with N. Costanzino, A. Mazzucato, AND V. Nistor, work in progress.

Finance/Mathematical Finance

1. Closed-form asymptotics and numerical approximations of 1D parabolic equations with applications to option pricing, with N. Costanzino, J. Liechty, A. Mazzucato, AND V. Nistor , 30 pages, SIAM Journal of Financial Mathematics (forthcoming). [PDF]

2. Closed Form Asymptotic Formulas for Time-varying Stochastic Volatility Models with Application to SABR and Heston, with R. Constantinescu, N. Costanzino, A. Mazzucato, AND V. Nistor, 31 pages, working paper, Aug. 2009

3. A Novel Heat Kernel Approach in Option Pricing, Model Calibration and Hedging, 41 pages, working paper, Dec. 2009

4..Approximate Solutions of 1D Parabolic Equations by a Neumann-Series Approach with Applications to Option Pricing, 21 pages, working paper, Jan. 2011.

5..Analytical Approximations in Option Pricing under Local Volatility Models, 20 pages, working paper, Jan. 2011.

6..An iterative algorithm in option pricing and portfolio management, work in progress.

7. Term structure modeling under Levy process, work in progress.

C++ Code for Derivative Pricing Click here

Talks

Option pricing by analytical approximations to solutions of parabolic PDEs, Financial Mathematics seminar, Penn State University, Feb. 2011
Closed-form asymptotics and numerical approximations of 1D parabolic equations with applications to option pricing, Mathematical Finance and Partial Differential Equations, Rutgers University, December, 2010.
A novel numerical method for a class of Cauchy problems, SIAM student seminar, Penn State University, September, 2010
Approximate solutions to second order parabolic equations, Conference on Applied Math, Rensselaer Polytechnic Institute , March, 2010.
Closed form approximation to parabolic equations with applications to finance, SIAM student seminar, Penn State University, October, 2009

Conferences

17 anual workshop on financial engineering, Nov. 19, 2010, Columbia University.
New Directions in Financial Mathematics, UCLA, January 5–8, 2010.
Mathematical Finance and Partial Differential Equations, Rutgers University, Dec. 5, 2009.
Special Session on Mathematical Finance, American Mathematical Society meetings, Penn State University, Oct 24–25, 2009

Teaching

Spring 2011, Math 251 Ordinary and Partial Differential Equations.
Course Homepage

Courses taught in the past

Awards

Departmental Teaching Award, Penn State U., 2011
University Graduate Fellowship, Penn Stte U., 2007-2008
First Prize, the International Mathematical Contest in Modeling, 2007
First Prize, the National Mathematical Contest in Modeling, China, 2007

Some Notes

Fundamentals of pseudodifferential operators
Semigroup theory with applications in PDE
Interpolation of Sobolev spaces

These notes aim to help my understanding during my study of the above subjects. I am still working on these notes to add some details and my own understanding. If you are a grad and never touch these subjects before, and you want to get some general ideas, you will find these notes useful. However, quality is not guaranteed. These notes, I think, will eventually go to the prelimilary part of my thesis.

Codes for Option pricing

Matlab code for Heston Model download
Matlab code for American option prcing under GBM download, also available here
Binomial tree method for the CEV model Matlab code
Monte Carlo method for the CEV model Matlab code
Link for option pricing

Other Stuff

Seminar on Probability and its Application
Mathematical Finance Seminar
SIAM student seminar at Penn State
Seminars at the PSU math department
Finance Journal Rating
Math finance conferences blog
Upcoming math finance conferences:
4th western conference on math finance
Old conferences:
New Directions in Financial Mathematics(Jan. 5-Jan. 8, 2010, UCLA)
Applied Math Days at RPI (March 19-March 20, 2010, RPI)
17 anual workshop on financial engineering (Nov. 19, 2010, Columbia Univ.)
Rutgers math finance and PDE conference (Dec. 10, 2010, NJ)
SIAM financial math conference (Nov. 19-20, SF)

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webpage managed by Wen Cheng. last update Dec. 13, 2010