From Local Volatility to Local Levy Models

Carr, Peter; Geman, Hélyette; Madan, Dilip B.; Yor, Marc

Download This Paper

Open PDF in Browser

Add Paper to My Library

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

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: 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