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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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    1. 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.
    2. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    3. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    4. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    5. John Y. Campbell & Albert S. Kyle, 1993. "Smart Money, Noise Trading and Stock Price Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(1), pages 1-34.
    6. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    7. repec:dau:papers:123456789/1448 is not listed on IDEAS
    8. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    9. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    10. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    11. Jean-Philippe Bouchaud & Andrew Matacz & Marc Potters, 2001. "The leverage effect in financial markets: retarded volatility and market panic," Science & Finance (CFM) working paper archive 0101120, Science & Finance, Capital Fund Management.
    12. repec:bla:jfinan:v:44:y:1989:i:1:p:211-19 is not listed on IDEAS
    13. repec:dau:papers:123456789/1392 is not listed on IDEAS
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