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Leveraged Levy processes as models for stock prices

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  • Dilip Madan
  • Yue Xiao

Abstract

Adopting a constant elasticity of variance formulation in the context of a general Levy process as the driving uncertainty we show that the presence of the leverage effect† in this form has the implication that asset price processes satisfy a scaling hypothesis. We develop forward partial integro-differential equations under a general Markovian setup, and show in two examples (both continuous and pure-jump Levy) how to use them for option pricing when stock prices follow our leveraged Levy processes. Using calibrated models we then show an example of simulation-based pricing and report on the adequacy of using leveraged Levy models to value equity structured products.

Suggested Citation

  • Dilip Madan & Yue Xiao, 2010. "Leveraged Levy processes as models for stock prices," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 735-748.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:7:p:735-748
    DOI: 10.1080/14697680903067138
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    References listed on IDEAS

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