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Option Pricing with Lévy-Stable Processes Generated by Lévy-Stable Integrated Variance

Author

Listed:
  • Alvaro Cartea

    (Department of Economics, Mathematics & Statistics, Birkbeck)

  • Sam Howison

Abstract

We show how to calculate European-style option prices when the log-stock price process follows a Levy-Stable process with index parameter 1 ≤ α ≤ 2 and skewness parameter -1 ≤ β ≤ 1. Key to our result is to model integrated variance [image omitted] as an increasing Levy-Stable process with continuous paths in T.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Alvaro Cartea & Sam Howison, 2006. "Option Pricing with Lévy-Stable Processes Generated by Lévy-Stable Integrated Variance," Birkbeck Working Papers in Economics and Finance 0602, Birkbeck, Department of Economics, Mathematics & Statistics.
  • Handle: RePEc:bbk:bbkefp:0602
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    File URL: http://www.bbk.ac.uk/ems/research/wp/PDF/BWPEF0602.pdf
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    References listed on IDEAS

    as
    1. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, April.
    2. Fama, Eugene F, 1971. "Risk, Return, and Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 79(1), pages 30-55, Jan.-Feb..
    3. 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.
    4. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    5. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
    6. Elisa Nicolato & Emmanouil Venardos, 2003. "Option Pricing in Stochastic Volatility Models of the Ornstein-Uhlenbeck type," Mathematical Finance, Wiley Blackwell, vol. 13(4), pages 445-466.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.

    More about this item

    Keywords

    Levy-Stable processes; stable Paretian hypothesis; stochastic volatility; alpha-stable processes; option pricing; time-changed Brownian motion.;

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