On the Data-Driven COS Method

Applied Mathematics and Computation 317: 68-84, 2018

26 Pages Posted: 16 Feb 2017 Last revised: 28 Oct 2018

See all articles by Alvaro Leitao Rodriguez

Alvaro Leitao Rodriguez

University of Coruña - Department of Mathematics - M2NICA

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI)

Luis Ortiz-Gracia

University of Barcelona

Sander Bohte

Center for Mathematics and Computer Science (CWI)

Date Written: February 15, 2017

Abstract

In this paper, we present the data-driven COS method, ddCOS. It is a Fourier-based financial option valuation method which assumes the availability of asset data samples: a characteristic function of the underlying asset probability density function is not required. As such, the method represents a generalization of the well-known COS method. Convergence with respect to the number of asset samples is according the convergence of Monte Carlo methods for pricing financial derivatives. The ddCOS method is particularly interesting for density recovery and also for the efficient computation of the option’s sensitivities Delta and Gamma. These are often used in risk management, and can be obtained at a higher accuracy with ddCOS than with plain Monte Carlo methods.

Keywords: Fourier, Density estimation, Statistical Learning theory, Greeks

JEL Classification: C16; C63

Suggested Citation

Leitao Rodriguez, Alvaro and Oosterlee, Cornelis W. and Ortiz-Gracia, Luis and Bohte, Sander, On the Data-Driven COS Method (February 15, 2017). Applied Mathematics and Computation 317: 68-84, 2018, Available at SSRN: https://ssrn.com/abstract=2917536 or http://dx.doi.org/10.2139/ssrn.2917536

Alvaro Leitao Rodriguez (Contact Author)

University of Coruña - Department of Mathematics - M2NICA ( email )

Campus Elvina s/n
A Coruna, 15071
Spain

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB
Netherlands

Luis Ortiz-Gracia

University of Barcelona ( email )

Diagonal, 690
08034 Barcelona
Spain

Sander Bohte

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB
Netherlands

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