From local volatility to local lévy models

Geman, Hélyette and Carr, P. and Madan, D.P. and Yor, M. (2004) From local volatility to local lévy models. Quantitative Finance 4 (5), pp. 581-588. ISSN 1469-7688.

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Official URL: http://dx.doi.org/10.1080/14697680400024921

Abstract

We define the class of local Lévy processes. These are Lévy 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 Lévy 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.

Metadata

Item Type:	Article
School:	Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School
Depositing User:	Sarah Hall
Date Deposited:	09 Jun 2020 06:58
Last Modified:	02 Aug 2023 18:00
URI:	https://eprints.bbk.ac.uk/id/eprint/32190

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