A QUASI-MONTE CARLO ALGORITHM FOR THE NORMAL INVERSE GAUSSIAN DISTRIBUTION AND VALUATION OF FINANCIAL DERIVATIVES

Fred Espen Benth (), Martin Groth () and Paul Kettler ()
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Fred Espen Benth: Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway;
Martin Groth: Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway

International Journal of Theoretical and Applied Finance (IJTAF), 2006, vol. 09, issue 06, 843-867

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.

Keywords: Quasi-Monte Carlo; normal inverse Gaussian distribution; Newton-Raphson method; option pricing; implied volatility (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0219024906003810

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