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Efficient Monte Carlo and quasi-Monte Carlo option pricing under the variance gamma model

Efficient Monte Carlo and quasi-Monte Carlo option pricing under the variance gamma model
Efficient Monte Carlo and quasi-Monte Carlo option pricing under the variance gamma model
We develop and study efficient Monte Carlo algorithms for pricing path-dependent options with the variance gamma model. The key ingredient is difference-of-gamma bridge sampling, based on the representation of a variance gamma process as the difference of two increasing gamma processes. For typical payoffs, we obtain a pair of estimators (named low and high) with expectations that (1) are monotone along any such bridge sampler, and (2) contain the continuous-time price. These estimators provide pathwise bounds on unbiased estimators that would be more expensive (infinitely expensive in some situations) to compute. By using these bounds with extrapolation techniques, we obtain significant efficiency improvements by work reduction. We then combine the gamma bridge sampling with randomized quasi–Monte Carlo to reduce the variance and thus further improve the efficiency. We illustrate the large efficiency improvements on numerical examples for Asian, lookback, and barrier options.
option pricing, efficiency improvement, extrapolation, quasi–monte carlo, variance gamma
0025-1909
1930-1944
Avramidis, A.N.
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001
L'Ecuyer, P.
6a72df10-5abf-4ff2-bb06-d9f9047f328e
Avramidis, A.N.
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001
L'Ecuyer, P.
6a72df10-5abf-4ff2-bb06-d9f9047f328e

Avramidis, A.N. and L'Ecuyer, P. (2006) Efficient Monte Carlo and quasi-Monte Carlo option pricing under the variance gamma model. Management Science, 52 (12), 1930-1944. (doi:10.1287/mnsc.1060.0575).

Record type: Article

Abstract

We develop and study efficient Monte Carlo algorithms for pricing path-dependent options with the variance gamma model. The key ingredient is difference-of-gamma bridge sampling, based on the representation of a variance gamma process as the difference of two increasing gamma processes. For typical payoffs, we obtain a pair of estimators (named low and high) with expectations that (1) are monotone along any such bridge sampler, and (2) contain the continuous-time price. These estimators provide pathwise bounds on unbiased estimators that would be more expensive (infinitely expensive in some situations) to compute. By using these bounds with extrapolation techniques, we obtain significant efficiency improvements by work reduction. We then combine the gamma bridge sampling with randomized quasi–Monte Carlo to reduce the variance and thus further improve the efficiency. We illustrate the large efficiency improvements on numerical examples for Asian, lookback, and barrier options.

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More information

Published date: December 2006
Keywords: option pricing, efficiency improvement, extrapolation, quasi–monte carlo, variance gamma
Organisations: Operational Research

Identifiers

Local EPrints ID: 48874
URI: https://eprints.soton.ac.uk/id/eprint/48874
ISSN: 0025-1909
PURE UUID: 575edf6d-1304-4d66-90a0-aada65040781

Catalogue record

Date deposited: 17 Oct 2007
Last modified: 13 Mar 2019 20:55

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