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Importance sampling for multimodal functions and application to pricing exotic options.

Importance sampling for multimodal functions and application to pricing exotic options.
Importance sampling for multimodal functions and application to pricing exotic options.
We consider importance sampling (IS) to increase the efficiency of Monte Carlo integration, especially for pricing exotic options where the random input is multivariate Normal. When the importance function (the product of integrand and original density) is multimodal, determining a good IS density is a difficult task. We propose an Automated Importance Sampling DEnsity selection procedure (AISDE). AISDE selects an IS density as a mixture of multivariate Normal densities with modes at certain local maxima of the importance function. When the simulation input is multivariate Normal, we use principal component analysis to obtain a reduced-dimension, approximate importance function, which allows efficient identification of a good IS density via AISDE in original problem dimensions over 100. We present Monte Carlo experimental results on randomly generated option-pricing problems (including path-dependent options), demonstrating large and consistent efficiency improvement.
AISDE Monte Carlo integration automated importance sampling density selection exotic options multimodal functions multivariate normal densities, multivariate normal random input, path-dependent options, pricing, principal component analysis, reduced-dimension importance function
0780376145
1493-1501
Avramidis, Athanassios.N.
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001
Yücesan, E.
dd6635e3-0c9e-4734-84f9-f14b7fa63d86
Chen, C.H.
bf06ddfe-d117-4a23-b6af-17911187f1f2
Snowdon, J. L.
eae87b18-44a5-409c-b7aa-5ad984c5ea79
Charnes, J. M.
91389e8d-4dfa-45d1-b4a2-421cbc30667a
Avramidis, Athanassios.N.
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001
Yücesan, E.
dd6635e3-0c9e-4734-84f9-f14b7fa63d86
Chen, C.H.
bf06ddfe-d117-4a23-b6af-17911187f1f2
Snowdon, J. L.
eae87b18-44a5-409c-b7aa-5ad984c5ea79
Charnes, J. M.
91389e8d-4dfa-45d1-b4a2-421cbc30667a

Avramidis, Athanassios.N. (2003) Importance sampling for multimodal functions and application to pricing exotic options. Yücesan, E., Chen, C.H., Snowdon, J. L. and Charnes, J. M. (eds.) 2002 Winter Simulation Conference, San Diego, USA. 08 - 11 Dec 2002. pp. 1493-1501 . (doi:10.1109/WSC.2002.1166424).

Record type: Conference or Workshop Item (Other)

Abstract

We consider importance sampling (IS) to increase the efficiency of Monte Carlo integration, especially for pricing exotic options where the random input is multivariate Normal. When the importance function (the product of integrand and original density) is multimodal, determining a good IS density is a difficult task. We propose an Automated Importance Sampling DEnsity selection procedure (AISDE). AISDE selects an IS density as a mixture of multivariate Normal densities with modes at certain local maxima of the importance function. When the simulation input is multivariate Normal, we use principal component analysis to obtain a reduced-dimension, approximate importance function, which allows efficient identification of a good IS density via AISDE in original problem dimensions over 100. We present Monte Carlo experimental results on randomly generated option-pricing problems (including path-dependent options), demonstrating large and consistent efficiency improvement.

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Published date: 22 January 2003
Venue - Dates: 2002 Winter Simulation Conference, San Diego, USA, 2002-12-08 - 2002-12-11
Keywords: AISDE Monte Carlo integration automated importance sampling density selection exotic options multimodal functions multivariate normal densities, multivariate normal random input, path-dependent options, pricing, principal component analysis, reduced-dimension importance function
Organisations: Operational Research

Identifiers

Local EPrints ID: 55790
URI: http://eprints.soton.ac.uk/id/eprint/55790
ISBN: 0780376145
PURE UUID: 12333605-cdf8-4690-a77b-0cbf4c8f6f74
ORCID for Athanassios.N. Avramidis: ORCID iD orcid.org/0000-0001-9310-8894

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Date deposited: 06 Aug 2008
Last modified: 12 Dec 2021 03:39

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Contributors

Editor: E. Yücesan
Editor: C.H. Chen
Editor: J. L. Snowdon
Editor: J. M. Charnes

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