Efficient simulation of gamma and variance-gamma processes
Efficient simulation of gamma and variance-gamma processes
We study algorithms for sampling discrete-time paths of a gamma process and a variance gamma process, defined as a Brownian process with random time change obeying a gamma process. The attractive feature of the algorithms is that increments of the processes over longer time scales are assigned to the first sampling coordinates. The algorithms are based on having in explicit form the process' conditional distributions, are similar in spirit to the Brownian bridge sampling algorithms proposed for financial Monte Carlo, and synergize with quasi-Monte Carlo techniques for efficiency improvement. We compare the variance and efficiency of ordinary Monte Carlo and quasi-Monte Carlo for an example of financial option pricing with the variance-gamma model, taken from fMAD98a.
Brownian bridge sampling algorithms Brownian process conditional distributions discrete-time path sampling efficiency improvement financial Monte Carlo financial option pricing gamma processes numerical integration process increments quasiMonte Carlo techniques, random time change, sampling coordinates, simulation, time scales, variance-gamma model, variance-gamma processes
0780381319
319-326
Avramidis, Athanassios.N.
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L'Ecuyer, Pierre
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Tremblay, Pierre-Alexandre
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Chick, S.
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Sánchez, P.J.
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Ferrin, D.
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Morrice, D.J.
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1 January 2004
Avramidis, Athanassios.N.
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001
L'Ecuyer, Pierre
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Tremblay, Pierre-Alexandre
3841b6d8-65eb-4908-8ec4-5b8320c0924e
Chick, S.
9e1d0dd9-fea9-46e5-9496-6913bf4340e6
Sánchez, P.J.
6f9e6061-e7e6-45e0-b035-14c11d6d3a18
Ferrin, D.
3de71b90-431b-4f84-8662-1d6f6a9c16b4
Morrice, D.J.
63f2baf8-80e9-4c6e-96e8-835158537187
Avramidis, Athanassios.N., L'Ecuyer, Pierre and Tremblay, Pierre-Alexandre
(2004)
Efficient simulation of gamma and variance-gamma processes.
Chick, S., Sánchez, P.J., Ferrin, D. and Morrice, D.J.
(eds.)
2003 Winter Simulation Conference, New Orleans, USA.
07 - 10 Dec 2003.
.
Record type:
Conference or Workshop Item
(Other)
Abstract
We study algorithms for sampling discrete-time paths of a gamma process and a variance gamma process, defined as a Brownian process with random time change obeying a gamma process. The attractive feature of the algorithms is that increments of the processes over longer time scales are assigned to the first sampling coordinates. The algorithms are based on having in explicit form the process' conditional distributions, are similar in spirit to the Brownian bridge sampling algorithms proposed for financial Monte Carlo, and synergize with quasi-Monte Carlo techniques for efficiency improvement. We compare the variance and efficiency of ordinary Monte Carlo and quasi-Monte Carlo for an example of financial option pricing with the variance-gamma model, taken from fMAD98a.
More information
Published date: 1 January 2004
Venue - Dates:
2003 Winter Simulation Conference, New Orleans, USA, 2003-12-07 - 2003-12-10
Keywords:
Brownian bridge sampling algorithms Brownian process conditional distributions discrete-time path sampling efficiency improvement financial Monte Carlo financial option pricing gamma processes numerical integration process increments quasiMonte Carlo techniques, random time change, sampling coordinates, simulation, time scales, variance-gamma model, variance-gamma processes
Organisations:
Operational Research
Identifiers
Local EPrints ID: 55793
URI: http://eprints.soton.ac.uk/id/eprint/55793
ISBN: 0780381319
PURE UUID: 75463371-c110-4110-8ec5-15bda9d84017
Catalogue record
Date deposited: 06 Aug 2008
Last modified: 16 Mar 2024 03:56
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Contributors
Author:
Pierre L'Ecuyer
Author:
Pierre-Alexandre Tremblay
Editor:
S. Chick
Editor:
P.J. Sánchez
Editor:
D. Ferrin
Editor:
D.J. Morrice
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