Leveraged Levy processes as models for stock prices

Dilip Madan and Yue Xiao

Quantitative Finance, 2010, vol. 10, issue 7, 735-748

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.

Keywords: Arbitrage pricing; Asset allocation; Asset pricing; Computational finance (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1080/14697680903067138

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