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Approximations for the distributions of bounded variation Lévy processes

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  • Figueroa-López, José E.

Abstract

We propose a feasible method for approximating the marginal distributions and densities of a bounded variation Lévy process using polynomial expansions. We provide a fast recursive formula for approximating the coefficients of the expansions and estimating the order of the approximation error. Our expansions are shown to be the exact counterpart of successive approximations of the Lévy process by compound Poisson processes previously proposed by, for instance, Barndorff-Nielsen and Hubalek (2008) [Barndorff-Nielsen, O.E., Hubalek, F., 2008. Probability measures, Lévy measures, and analyticity in time. Bernoulli 3 (14), 764-790] and others, and hence, give an answer to an open problem raised therein.

Suggested Citation

  • Figueroa-López, José E., 2010. "Approximations for the distributions of bounded variation Lévy processes," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1744-1757, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1744-1757
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Figueroa-López, José E. & Houdré, Christian, 2009. "Small-time expansions for the transition distributions of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3862-3889, November.
    3. Andrew Matacz, 2000. "Financial Modeling And Option Theory With The Truncated Levy Process," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 143-160.
    4. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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