Option pricing with Legendre polynomials

Article


Hok, Julien and Chan, R. 2017. Option pricing with Legendre polynomials. Journal of Computational and Applied Mathematics. 322, pp. 25-45.
AuthorsHok, Julien and Chan, R.
Abstract

Here we develop an option pricing method based on Legendre series expansion of the density function. The key insight, relying on the close relation of the characteristic function with the series coefficients, allows to recover the density function rapidly and accurately. Based on this representation for the density function, approximations formulas for pricing European type options are derived. To obtain highly accurate result for European call option, the implementation involves integrating high degree Legendre polynomials against exponential function. Some numerical instabilities arise because of serious subtractive cancellations in its formulation (96) in Proposition A.1. To overcome this difficulty, we rewrite this quantity as solution of a second-order linear difference equation and solve it using a robust and stable algorithm from Olver. Derivation of the pricing method has been accompanied by an error analysis. Errors bounds have been derived and the study relies more on smoothness properties which are not provided by the payoff functions, but rather by the density function of the underlying stochastic models. This is particularly relevant for options pricing where the payoffs of the contract are generally not smooth functions. The numerical experiments on a class of models widely used in quantitative finance show exponential convergence.

JournalJournal of Computational and Applied Mathematics
Journal citation322, pp. 25-45
ISSN03770427
Year2017
PublisherElsevier for North-Holland Publishing
Accepted author manuscript
License
Digital Object Identifier (DOI)doi:10.1016/j.cam.2017.03.027
Web address (URL)https://doi.org/10.1016/j.cam.2017.03.027
Publication dates
Online30 Mar 2017
Publication process dates
Deposited01 Dec 2017
LicenseCC BY-NC-ND 4.0
Permalink -

https://repository.uel.ac.uk/item/84w98

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