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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.

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Bibliographic Info

Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2002mf04.

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Date of creation: 2002
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Handle: RePEc:sbs:wpsefe:2002mf04

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Web page: http://www.finance.ox.ac.uk
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Cited by:
  1. Przemys{\l}aw Repetowicz & Peter Richmond, 2006. "Option pricing with log-stable L\'{e}vy processes," Papers math/0612691, arXiv.org.
  2. 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.
  3. 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.
  4. 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.

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