NDLI: Levy Process Simulation by Stochastic Step Functions

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Benth, Fred Espen Srensen, Torquil Macdonald
Copyright Year	2013
Abstract	We study a Monte Carlo algorithm for simulation of probability distributions based on stochastic step functions, and compare it to the traditional Metropolis/Hastings method. Unlike the latter, the step function algorithm can produce an uncorrelated Markov chain. We apply this method to the simulation of Levy processes, for which drawing of uncorrelated jumps is essential. We perform numerical tests consisting of simulation from probability distributions, as well as simulation of Levy process paths. The Levy processes include a jump diffusion with a Gaussian Levy measure, as well as jump-diffusion approximations of the infinite activity normal inverse Gaussian (NIG) and CGMY processes. To increase efficiency of the step function method, and to decrease correlations in the Metropolis/Hastings method, we introduce adaptive hybrid algorithms which employ uncorrelated draws from an adaptive discrete distribution defined on a subdivision of the Levy measure space. The nonzero correlations in Metropolis/Hastings simulations result in heavy tails for the Levy process distribution at any fixed time. This problem is eliminated in the step function approach. In each case of the Gaussian, NIG, and CGMY processes, we compare the distribution at $t=1$ with exact results and note the superiority of the step function approach, as well as the autocorrelation functions.
Starting Page	A2207
Ending Page	A2224
Page Count	18
File Format	PDF
ISSN	10648275
DOI	10.1137/110851080
e-ISSN	10957197
Issue Number	5
Volume Number	35
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-09-26
Access Restriction	Subscribed
Subject Keyword	Monte Carlo methods Time series, auto-correlation, regression, etc. Jump processes Levy process Markov chains Computational methods in Markov chains simulation of probability distributions Sample path properties Processes with independent increments; Lévy processes
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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