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Finite element based Monte Carlo simulation of options on Lévy driven assets

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  • Patrik Karlsson

    (Department of Economics, Lund University, Box 7082, SE-22007 Lund, Sweden2Quantitative Strategy and Analytics, SEB, Kungstradgardsgatan 8, SE-106 40 Stockholm, Sweden)

Abstract

This paper extends the simulation algorithm by Andreasen and Huge (2011) to the simulation of option prices and deltas on Lévy driven assets where the simulation is performed relying on the inverse transition matrix of the discretized partial integro differential equation (PIDE). We demonstrate how one can get accurate prices and deltas of European options on VG and CGMY via Monte Carlo simulations.

Suggested Citation

  • Patrik Karlsson, 2018. "Finite element based Monte Carlo simulation of options on Lévy driven assets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-23, March.
    • Handle: RePEc:wsi:ijfexx:v:05:y:2018:i:01:n:s2424786318500135
    DOI: 10.1142/S2424786318500135
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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.
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    5. 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.
    6. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Brennan, Michael J. & Schwartz, Eduardo S., 1978. "Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(3), pages 461-474, September.
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    Cited by:

    1. Søren Asmussen, 2022. "On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance," Finance and Stochastics, Springer, vol. 26(3), pages 383-416, July.

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