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Distinguished Limits of Levy-Stable Processes, and Applications to Option Pricing

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  • Alvaro Cartea
  • Sam Howison

Abstract

In this paper we derive analytic expressions for the value of European Put and Call options when the stock process follows an exponential Levy-Stable process. It is shown that the generalised Black-Scholes operator for the Levy-Stable case can be obtained as an asymptotic approximation of a process where the random variable follows a damped Levy process. Finally, it is also shown that option prices under the Levy-Stable case generate the volatility smile encountered in the financial markets when the Black-Scholes framework is employed.

Suggested Citation

  • Alvaro Cartea & Sam Howison, 2002. "Distinguished Limits of Levy-Stable Processes, and Applications to Option Pricing," OFRC Working Papers Series 2002mf04, Oxford Financial Research Centre.
  • Handle: RePEc:sbs:wpsefe:2002mf04
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    File URL: http://www.finance.ox.ac.uk/file_links/finecon_papers/2002mf04.pdf
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    Cited by:

    1. Alvaro Cartea & Sam Howison, 2009. "Option pricing with Levy-Stable processes generated by Levy-Stable integrated variance," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 397-409.
    2. J. Huston McCulloch, 2003. "The Risk-Neutral Measure and Option Pricing under Log-Stable Uncertainty," Working Papers 03-07, Ohio State University, Department of Economics.
    3. J. Huston McCulloch, 2004. "The Risk-Neutral Measure and Option Pricing under Log-Stable Uncertainty using Romberg Fourier Inversion," Computing in Economics and Finance 2004 13, Society for Computational Economics.
    4. Przemys{l}aw Repetowicz & Peter Richmond, 2006. "Option pricing with log-stable L\'{e}vy processes," Papers math/0612691, arXiv.org.

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