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From Local Volatility to Local Levy Models

Yor, Marc; Madan, Dilip B.; Carr, Peter; Geman, Hélyette (2004), From Local Volatility to Local Levy Models, Quantitative Finance, 4, 5, p. 581-588

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Type
Article accepté pour publication ou publié
Date
2004-10
Journal name
Quantitative Finance
Volume
4
Number
5
Publisher
Routledge
Pages
581-588
Metadata
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Author(s)
Yor, Marc
Madan, Dilip B.
Carr, Peter
Geman, Hélyette
Abstract (EN)
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.
Subjects / Keywords
Levy processes; Derivatives securities; Random walks (mathematics); Volatility (finance); Options (finance)
JEL
G11 - Portfolio Choice; Investment Decisions