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Convergence of the stochastic mesh estimator for pricing American options

Convergence of the stochastic mesh estimator for pricing American options
Convergence of the stochastic mesh estimator for pricing American options
Broadie and Glasserman proposed a simulation-based method they named {\em stochastic mesh} for pricing high-dimensional American options. Based on simulated states of the assets underlying the option at each exercise opportunity, the method produces an estimator of the option value at each sampled state. Under the mild assumption of the finiteness of certain moments, we derive an asymptotic upper bound on the probability of error of the mesh estimator, where both the error size and the probability bound vanish as the sample size increases. We include the empirical performance for the test problems used by Broadie and Glasserman in a recent unpublished manuscript. We find that the mesh estimator has large bias that decays very slowly with the sample size, suggesting that in applications it will most likely be necessary to employ bias and/or variance reduction techniques.
0780376145
1560-1567
Avramidis, Athanassios
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001
Matzinger, Heinrich
397d839a-11d9-4c8d-a9eb-980f399e81f0
Avramidis, Athanassios
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001
Matzinger, Heinrich
397d839a-11d9-4c8d-a9eb-980f399e81f0

Avramidis, Athanassios and Matzinger, Heinrich (2002) Convergence of the stochastic mesh estimator for pricing American options. 2002 Winter Simulation Conference, San Diego, USA. 08 - 11 Dec 2002. pp. 1560-1567 . (doi:10.1109/WSC.2002.1166433).

Record type: Conference or Workshop Item (Other)

Abstract

Broadie and Glasserman proposed a simulation-based method they named {\em stochastic mesh} for pricing high-dimensional American options. Based on simulated states of the assets underlying the option at each exercise opportunity, the method produces an estimator of the option value at each sampled state. Under the mild assumption of the finiteness of certain moments, we derive an asymptotic upper bound on the probability of error of the mesh estimator, where both the error size and the probability bound vanish as the sample size increases. We include the empirical performance for the test problems used by Broadie and Glasserman in a recent unpublished manuscript. We find that the mesh estimator has large bias that decays very slowly with the sample size, suggesting that in applications it will most likely be necessary to employ bias and/or variance reduction techniques.

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More information

Published date: 2002
Venue - Dates: 2002 Winter Simulation Conference, San Diego, USA, 2002-12-08 - 2002-12-11
Organisations: Operational Research

Identifiers

Local EPrints ID: 55789
URI: http://eprints.soton.ac.uk/id/eprint/55789
ISBN: 0780376145
PURE UUID: f41ab270-31a4-4cc9-aee2-9b37958fec34
ORCID for Athanassios Avramidis: ORCID iD orcid.org/0000-0001-9310-8894

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Date deposited: 06 Aug 2008
Last modified: 18 Feb 2021 17:10

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