From local volatility to local Lévy models

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

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)581-588
Number of pages8
JournalQuantitative Finance
Volume4
Issue number5
DOIs
StatePublished - Oct 2004

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Local volatility
Lévy process
Maturity
Volatility models
Option prices
Engineers
Time-changed Lévy processes
Numerical methods

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance(all)

Cite this

Carr, P., Geman, H., Madan, D. B., & Yor, M. (2004). From local volatility to local Lévy models. Quantitative Finance, 4(5), 581-588. https://doi.org/10.1080/14697680400024921

From local volatility to local Lévy models. / Carr, Peter; Geman, Hélyette; Madan, Dilip B.; Yor, Marc.

In: Quantitative Finance, Vol. 4, No. 5, 10.2004, p. 581-588.

Research output: Contribution to journalArticle

Carr, P, Geman, H, Madan, DB & Yor, M 2004, 'From local volatility to local Lévy models', Quantitative Finance, vol. 4, no. 5, pp. 581-588. https://doi.org/10.1080/14697680400024921
Carr, Peter ; Geman, Hélyette ; Madan, Dilip B. ; Yor, Marc. / From local volatility to local Lévy models. In: Quantitative Finance. 2004 ; Vol. 4, No. 5. pp. 581-588.
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