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Option pricing with Levy-Stable processes generated by Levy-Stable integrated variance

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  • Alvaro Cartea
  • 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.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:quantf:v:9:y:2009:i:4:p:397-409
    DOI: 10.1080/14697680902748506
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    1. Yesim Tokat & Eduardo S. Schwartz, 2002. "The impact of fat tailed returns on asset allocation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 165-185, May.
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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.
    2. Álvaro Cartea, 2013. "Derivatives pricing with marked point processes using tick-by-tick data," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 111-123, January.

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