Pricing European-type, early-exercise and discrete barrier options using an algorithm for the convolution of Legendre series
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.
|Authors||Chan, R. and Hale, N.|
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.
|Publisher||Taylor & Francis|
|Accepted author manuscript|
File Access Level
|Digital Object Identifier (DOI)||doi:10.1080/14697688.2020.1736612|
|Web address (URL)||https://doi.org/10.1080/14697688.2020.1736612|
|Online||07 Apr 2020|
|Publication process dates|
|Accepted||17 Feb 2020|
|Deposited||04 May 2020|
|Copyright holder||© 2020 Taylor & Francis|
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.
Accepted author manuscript
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