Efficient Numerical Inversion for Financial Simulations

Gerhard Derflinger; Wolfgang Hörmann; Josef Leydold; Halis Sak

Efficient Numerical Inversion for Financial Simulations

Gerhard Derflinger, Wolfgang Hörmann, Josef Leydold, Halis Sak

Publication: Chapter in book/Conference proceeding › Contribution to conference proceedings

Abstract

Generating samples from generalized hyperbolic distributions and non-central chi-square distributions by inversion has become an important task for the simulation of recent models in finance in the framework of (quasi-) Monte Carlo.
However, their distribution functions are quite expensive to evaluate and thus numerical methods like root finding algorithms are extremely slow.
In this paper we demonstrate how our new method based on Newton inter-polation and Gauss-Lobatto quadrature can be utilized for financial applications.
Its fast marginal generation times make it competitive, even for situations where the parameters are not always constant.

Original language	English
Title of host publication	Monte Carlo and Quasi-Monte Carlo Methods 2008
Editors	Pierre L'Ecuyer and Art B. Owen
Place of Publication	Berlin
Publisher	Springer
Pages	297 - 304
Publication status	Published - 1 Dec 2009

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1 WU Working Paper

Efficient Numerical Inversion for Financial Simulations
Derflinger, G., Hörmann, W., Leydold, J. & Sak, H., 1 Jun 2009, (Research Report Series / Department of Statistics and Mathematics; No. 87).
Publication: Working/Discussion Paper › WU Working Paper

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abstract = "Generating samples from generalized hyperbolic distributions and non-central chi-square distributions by inversion has become an important task for the simulation of recent models in finance in the framework of (quasi-) Monte Carlo. However, their distribution functions are quite expensive to evaluate and thus numerical methods like root finding algorithms are extremely slow. In this paper we demonstrate how our new method based on Newton inter-polation and Gauss-Lobatto quadrature can be utilized for financial applications. Its fast marginal generation times make it competitive, even for situations where the parameters are not always constant.",

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N2 - Generating samples from generalized hyperbolic distributions and non-central chi-square distributions by inversion has become an important task for the simulation of recent models in finance in the framework of (quasi-) Monte Carlo. However, their distribution functions are quite expensive to evaluate and thus numerical methods like root finding algorithms are extremely slow. In this paper we demonstrate how our new method based on Newton inter-polation and Gauss-Lobatto quadrature can be utilized for financial applications. Its fast marginal generation times make it competitive, even for situations where the parameters are not always constant.

AB - Generating samples from generalized hyperbolic distributions and non-central chi-square distributions by inversion has become an important task for the simulation of recent models in finance in the framework of (quasi-) Monte Carlo. However, their distribution functions are quite expensive to evaluate and thus numerical methods like root finding algorithms are extremely slow. In this paper we demonstrate how our new method based on Newton inter-polation and Gauss-Lobatto quadrature can be utilized for financial applications. Its fast marginal generation times make it competitive, even for situations where the parameters are not always constant.

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BT - Monte Carlo and Quasi-Monte Carlo Methods 2008

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Efficient Numerical Inversion for Financial Simulations

Abstract

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Efficient Numerical Inversion for Financial Simulations

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