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Financial Modeling and Option Theory with the Truncated Levy Process

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  • Andrew Matacz

    (University of Sydney, Australia)

Abstract

In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed excess kurtosis at short timescales, along with the slow convergence to Gaussian at longer timescales. I further test the truncated Levy paradigm using high frequency data from the Australian All Ordinaries share market index. I then consider, for the early Levy dominated regime, the issue of option hedging for two different hedging strategies that are in some sense optimal. These are compared with the usual delta hedging approach and found to differ significantly. I also derive the natural generalization of the Black-Scholes option pricing formula when the underlying security is modeled by a geometric TLP. This generalization would not be possible without the truncation.

Suggested Citation

  • Andrew Matacz, 1997. "Financial Modeling and Option Theory with the Truncated Levy Process," Papers cond-mat/9710197, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/9710197
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    Cited by:

    1. Schultze, Uta, 2000. "Insights from Physics into Development Processes: Are Fat Tails Interesting for Development Research?," Discussion Papers 280882, University of Bonn, Center for Development Research (ZEF).
    2. Skjeltorp, Johannes A, 2000. "Scaling in the Norwegian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(3), pages 486-528.
    3. Stanley, H.E & Amaral, L.A.N & Canning, D & Gopikrishnan, P & Lee, Y & Liu, Y, 1999. "Econophysics: Can physicists contribute to the science of economics?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 156-169.

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