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A Quasi-Monte Carlo Algorithm For The Normal Inverse Gaussian Distribution And Valuation Of Financial Derivatives

Author

Listed:
  • FRED ESPEN BENTH

    (Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway;
    Agder University College, School of Management, Serviceboks 422, N-4604 Kristiansand, Norway)

  • MARTIN GROTH

    (Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway)

  • PAUL C. KETTLER

    (Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway)

Abstract

We propose a quasi-Monte Carlo (qMC) algorithm to simulate variates from the normal inverse Gaussian (NIG) distribution. The algorithm is based on a Monte Carlo technique found in Rydberg [13], and is based on sampling three independent uniform variables. We apply the algorithm to three problems appearing in finance. First, we consider the valuation of plain vanilla call options and Asian options. The next application considers the problem of deriving implied parameters for the underlying asset dynamics based on observed option prices. We employ our proposed algorithm together with the Newton Method, and show how we can find the scale parameter of the NIG-distribution of the logreturns in case of a call or an Asian option. We also provide an extensive error analysis for this method. Finally we study the calculation of Value-at-Risk for a portfolio of nonlinear products where the returns are modeled by NIG random variables.

Suggested Citation

  • Fred Espen Benth & Martin Groth & Paul C. Kettler, 2006. "A Quasi-Monte Carlo Algorithm For The Normal Inverse Gaussian Distribution And Valuation Of Financial Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(06), pages 843-867.
    • Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:06:n:s0219024906003810
    DOI: 10.1142/S0219024906003810
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    Cited by:

    1. Jan Baldeaux & Dale Roberts, 2012. "Quasi-Monte Carlo methods for the Heston model," Papers 1202.3217, arXiv.org, revised May 2012.
    2. Khaled Salhi, 2017. "Pricing European options and risk measurement under exponential Lévy models — a practical guide," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-36, June.

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