Quasi-Monte Carlo Simulation of Discrete-Time Markov Chains on Multidimensional State Spaces

Rami El Haddad (), Christian Lécot () and Pierre L’Ecuyer ()
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Rami El Haddad: Université Saint-Joseph, Département de Mathématiques
Christian Lécot: Université de Savoie, LAMA
Pierre L’Ecuyer: Université de Montréal, DIRO

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2006, 2008, pp 413-429 from Springer

Abstract: Summary We propose and analyze a quasi-Monte Carlo (QMC) method for simulating a discrete-time Markov chain on a discrete state space of dimension s ≥ 1. Several paths of the chain are simulated in parallel and reordered at each step, using a multidimensional matching between the QMC points and the copies of the chains. This method generalizes a technique proposed previously for the case where s = 1. We provide a convergence result when the number N of simulated paths increases toward infinity. Finally, we present the results of some numerical experiments showing that our QMC algorithm converges faster as a function of N, at least in some situations, than the corresponding Monte Carlo (MC) method.

Keywords: Monte Carlo; Option Price; Risky Asset; Elementary Interval; Simple Symmetric Random Walk (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-74496-2_24

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DOI: 10.1007/978-3-540-74496-2_24

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