From Local Volatility to Local Levy Models

Quantitative Finance, Vol. 4, No. 5, October 2004

17 Pages Posted: 15 Jan 2007

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Hélyette Geman

University of London - Economics, Mathematics and Statistics

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Marc Yor

Universite Paris

Abstract

We define the class of local Levy processes. These are Levy processes time changed by an inhomogeneous local speed function. The local speed function is a deterministic function of time and the level of the process itself. We show how to reverse engineer the local speed function from traded option prices of all strikes and maturities. The local Levy processes generalize the class of local volatility models. Closed forms for local speed functions for a variety of cases are also presented. Numerical methods for recovery are also described.

Keywords: Hunt Processes, Persistent Skewness, Convolution Transforms

JEL Classification: G10, G12, G13

Suggested Citation

Carr, Peter P. and Geman, Helyette and Madan, Dilip B. and Yor, Marc, From Local Volatility to Local Levy Models. Quantitative Finance, Vol. 4, No. 5, October 2004. Available at SSRN: https://ssrn.com/abstract=957170

Peter P. Carr

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Helyette Geman

University of London - Economics, Mathematics and Statistics ( email )

Malet Street
London, WC1E 7HX
United Kingdom

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

Marc Yor

Universite Paris ( email )

223 Rue Saint-Honore
Paris, 75775
France

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