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From local volatility to local Levy models

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  • Peter Carr
  • Helyette Geman
  • Dilip Madan
  • Marc Yor
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    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.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 4 (2004)
    Issue (Month): 5 ()
    Pages: 581-588

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    Handle: RePEc:taf:quantf:v:4:y:2004:i:5:p:581-588

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    Cited by:
    1. Samuel N. Cohen & Lukasz Szpruch, 2011. "On Markovian solutions to Markov Chain BSDEs," Papers 1111.5739, arXiv.org.
    2. Eckhard Platen & Renata Rendek, 2012. "The Affine Nature of Aggregate Wealth Dynamics," Research Paper Series 322, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Peter K. Friz & Stefan Gerhold & Marc Yor, 2013. "How to make Dupire's local volatility work with jumps," Papers 1302.5548, arXiv.org.
    4. Madan, D. & Roynette, B. & Yor, Marc, 2008. "Option prices as probabilities," Finance Research Letters, Elsevier, vol. 5(2), pages 79-87, June.

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