Smoothing the payoff for efficient computation of Basket option prices

Handle URI:
http://hdl.handle.net/10754/626067
Title:
Smoothing the payoff for efficient computation of Basket option prices
Authors:
Bayer, Christian; Siebenmorgen, Markus; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
We consider the problem of pricing basket options in a multivariate Black–Scholes or Variance-Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high-dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical integration techniques may not be directly available, requiring the use of methods like Monte Carlo specifically designed to work for non-regular problems. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. The resulting conditional expectation is unbiased and yields a smooth integrand, which is amenable to the efficient use of adaptive sparse-grid cubature. Numerical examples indicate that the high-order method may perform orders of magnitude faster than Monte Carlo or Quasi Monte Carlo methods in dimensions up to 35.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Bayer C, Siebenmorgen M, Tempone R (2017) Smoothing the payoff for efficient computation of Basket option prices. Quantitative Finance: 1–15. Available: http://dx.doi.org/10.1080/14697688.2017.1308003.
Publisher:
Informa UK Limited
Journal:
Quantitative Finance
Issue Date:
22-Jul-2017
DOI:
10.1080/14697688.2017.1308003
Type:
Article
ISSN:
1469-7688; 1469-7696
Sponsors:
King Abdullah University of Science and Technology[CEMSE]
Additional Links:
http://www.tandfonline.com/doi/abs/10.1080/14697688.2017.1308003
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBayer, Christianen
dc.contributor.authorSiebenmorgen, Markusen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2017-10-31T11:17:11Z-
dc.date.available2017-10-31T11:17:11Z-
dc.date.issued2017-07-22en
dc.identifier.citationBayer C, Siebenmorgen M, Tempone R (2017) Smoothing the payoff for efficient computation of Basket option prices. Quantitative Finance: 1–15. Available: http://dx.doi.org/10.1080/14697688.2017.1308003.en
dc.identifier.issn1469-7688en
dc.identifier.issn1469-7696en
dc.identifier.doi10.1080/14697688.2017.1308003en
dc.identifier.urihttp://hdl.handle.net/10754/626067-
dc.description.abstractWe consider the problem of pricing basket options in a multivariate Black–Scholes or Variance-Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high-dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical integration techniques may not be directly available, requiring the use of methods like Monte Carlo specifically designed to work for non-regular problems. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. The resulting conditional expectation is unbiased and yields a smooth integrand, which is amenable to the efficient use of adaptive sparse-grid cubature. Numerical examples indicate that the high-order method may perform orders of magnitude faster than Monte Carlo or Quasi Monte Carlo methods in dimensions up to 35.en
dc.description.sponsorshipKing Abdullah University of Science and Technology[CEMSE]en
dc.publisherInforma UK Limiteden
dc.relation.urlhttp://www.tandfonline.com/doi/abs/10.1080/14697688.2017.1308003en
dc.rightsThis is an Accepted Manuscript of an article published by Taylor & Francis in Quantitative Finance on 20 Jul 2017, available online: http://wwww.tandfonline.com/10.1080/14697688.2017.1308003.en
dc.subjectComputational Financeen
dc.subjectEuropean option pricingen
dc.subjectMonte Carlo and Quasi Monte Carlo methodsen
dc.subjectMultivariate approximation and integrationen
dc.subjectSparse gridsen
dc.subjectStochastic Collocation methodsen
dc.titleSmoothing the payoff for efficient computation of Basket option pricesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalQuantitative Financeen
dc.eprint.versionPost-printen
dc.contributor.institutionWeierstrass Institute, Mohrenstrasse 39, 10117Berlin, Germany.en
dc.contributor.institutionInstitute for Numerical Simulation, University of Bonn, Wegelerstr. 6, 53115Bonn, Germany.en
kaust.authorTempone, Raulen
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