Pricing European-type, early-exercise and discrete barrier options using an algorithm for the convolution of Legendre series

Article


Chan, R. and Hale, N. 2020. Pricing European-type, early-exercise and discrete barrier options using an algorithm for the convolution of Legendre series. Quantitative Finance.
AuthorsChan, R. and Hale, N.
Abstract

This paper applies an algorithm for the convolution of compactly supported Legendre series (the CONLeg method) (cf. Hale and Townsend, An algorithm for the convolution of Legendre series. SIAM J. Sci. Comput., 2014, 36, A1207–A1220), to pricing European-type, early-exercise and discrete-monitored barrier options under a Lévy process. The paper employs Chebfun (cf. Trefethen et al., Chebfun Guide, 2014 (Pafnuty Publications: Oxford), Available online at: http://www.chebfun.org/) in computational finance and provides a quadrature-free approach by applying the Chebyshev series in financial modelling. A significant advantage of using the CONLeg method is to formulate option pricing and option Greek curves rather than individual prices/values. Moreover, the CONLeg method can yield high accuracy in option pricing when the risk-free smooth probability density function (PDF) is smooth/non-smooth. Finally, we show that our method can accurately price options deep in/out of the money and with very long/short maturities. Compared with existing techniques, the CONLeg method performs either favourably or comparably in numerical experiments.

JournalQuantitative Finance
ISSN1469-7688
Year2020
PublisherTaylor & Francis
Accepted author manuscript
License
File Access Level
Anyone
Digital Object Identifier (DOI)doi:10.1080/14697688.2020.1736612
Web address (URL)https://doi.org/10.1080/14697688.2020.1736612
Publication dates
Online07 Apr 2020
Publication process dates
Accepted17 Feb 2020
Deposited04 May 2020
Copyright holder© 2020 Taylor & Francis
Additional information

This is an Accepted Manuscript of an article published by Taylor & Francis in Quantitative Finance on 07/04/2020, available online: https://doi.org/10.1080/14697688.2020.1736612.

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