Conformal Accelerations Method and Efficient Evaluation of Stable Distributions

26 Pages Posted: 24 Jul 2018 Last revised: 13 Aug 2018

See all articles by Svetlana Boyarchenko

Svetlana Boyarchenko

University of Texas at Austin - Department of Economics

Sergei Levendorskii

Calico Science Consulting

Date Written: July 2, 2018

Abstract

We suggest new efficient integral representations and methods for evaluation of pdfs, cpds and quantiles of stable distributions. For wide regions in the parameter space, absolute errors of order 10 can be achieved in 0.005-0.1 msec (Matlab implementation), even when the index of the distribution is small or close to 1. For the calculation of quantiles in wide regions in the tails using the Newton or bisection method, it suffices to precompute several hundred values of the characteristic exponent at points of an appropriate grid (conformal principal components) and use these values in formulas for cpdf and pdf, which require a fairly small number of elementary operations. The methods of the paper are applicable to other classes of integrals, especially highly oscillatory ones, and are typically faster than the popular methods.

Keywords: Stable Levy Processes, Monte Carlo Simulations, Conformal Principal Components, Sinh-Acceleration, Simplified Trapezoid Rule, Simplified Conic Trapezoid Rule, Richardson Extrapolation, Signal Processing

JEL Classification: C02

Suggested Citation

Boyarchenko, Svetlana I. and Levendorskii, Sergei Z., Conformal Accelerations Method and Efficient Evaluation of Stable Distributions (July 2, 2018). Available at SSRN: https://ssrn.com/abstract=3206696 or http://dx.doi.org/10.2139/ssrn.3206696

Svetlana I. Boyarchenko

University of Texas at Austin - Department of Economics ( email )

Austin, TX 78712
United States

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

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