Closed-Form Asymptotics for Local Volatility Models

30 Pages Posted: 12 Oct 2009 Last revised: 23 Apr 2010

See all articles by Wen Cheng

Wen Cheng

Pennsylvania State University - Department of Mathematics

Nick Costanzino

Barclays Capital; New York University - Department of Finance and Risk Enginieering

Anna L. Mazzucato

Pennsylvania State University

John Liechty

Pennsylvania State University, University Park

Victor Nistor

Department of Mathematics; Pennsylvania State University

Date Written: October 9, 2009

Abstract

We obtain new closed-form pricing formulas for contingent claims when the asset follows a Dupire-type local volatility model. To obtain the formulas we use the Dyson-Taylor commutator method recently developed in [7, 8, 10] for short time asymptotic expansions of heat kernels, and obtain a family of general explicit closed form approximate solutions for both the pricing kernel and derivative price. We also perform analytic as well as a numerical error analysis, and compare our results to other known methods.

Keywords: derivative pricing, local volatility models, closed form solutions, asymptotics

Suggested Citation

Cheng, Wen and Costanzino, Nick and Mazzucato, Anna L. and Liechty, John and Nistor, Victor, Closed-Form Asymptotics for Local Volatility Models (October 9, 2009). Available at SSRN: https://ssrn.com/abstract=1486470 or http://dx.doi.org/10.2139/ssrn.1486470

Wen Cheng

Pennsylvania State University - Department of Mathematics ( email )

University Park
State College, PA 16802
United States

HOME PAGE: http://www.math.psu.edu/cheng

Nick Costanzino (Contact Author)

Barclays Capital ( email )

745 7th Ave
Floor 2
New York, NY
United States

New York University - Department of Finance and Risk Enginieering

Brooklyn, NY 11201
United States

Anna L. Mazzucato

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

John Liechty

Pennsylvania State University, University Park ( email )

University Park
State College, PA 16802
United States

Victor Nistor

Department of Mathematics ( email )

Ile du Saulcy
57045 Metz, cedex 1
France

HOME PAGE: http://iecl.univ-lorraine.fr/~Victor.Nistor/index.htm

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

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