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From local volatility to local Levy models

Author

Listed:
  • Peter Carr
  • Helyette Geman
  • Dilip Madan
  • Marc Yor

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.

Suggested Citation

  • Peter Carr & Helyette Geman & Dilip Madan & Marc Yor, 2004. "From local volatility to local Levy models," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 581-588.
    • Handle: RePEc:taf:quantf:v:4:y:2004:i:5:p:581-588
    DOI: 10.1080/14697680400000039
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