Smoothing the payoff for efficient computation of Basket option prices
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2017-07-22Permanent link to this record
http://hdl.handle.net/10754/626067
Metadata
Show full item recordAbstract
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.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.Sponsors
King Abdullah University of Science and Technology[CEMSE]Publisher
Informa UK LimitedJournal
Quantitative FinancearXiv
1607.05572Additional Links
http://www.tandfonline.com/doi/abs/10.1080/14697688.2017.1308003ae974a485f413a2113503eed53cd6c53
10.1080/14697688.2017.1308003