An Improved Convolution Algorithm for Discretely Sampled Asian Options

19 Pages Posted: 5 Jan 2009 Last revised: 4 Nov 2013

See all articles by Aleš Černý

Aleš Černý

Cass Business School, City, University of London

Ioannis Kyriakou

City University London - Sir John Cass Business School

Abstract

We suggest an improved FFT pricing algorithm for discretely sampled Asian options with general independently distributed returns in the underlying. Our work complements the studies of Carverhill and Clewlow (1992), Benhamou (2000), and Fusai and Meucci (2008), and, if we restrict our attention only to lognormally distributed returns, also Vecer (2002). While the existing convolution algorithms compute the density of the underlying state variable by moving forward on a suitably defined state space grid our new algorithm uses backward price convolution, which resembles classical lattice pricing algorithms. For the first time in the literature we provide an analytical upper bound for the pricing error caused by the truncation of the state space grid and by the curtailment of the integration range. We highlight the benefits of the new scheme and benchmark its performance against existing finite difference, Monte Carlo, and forward density convolution algorithms.

Keywords: Asian options, Discrete sampling, Convolution, FFT

JEL Classification: G12, G13, C63

Suggested Citation

Černý, Aleš and Kyriakou, Ioannis, An Improved Convolution Algorithm for Discretely Sampled Asian Options. Quantitative Finance, 2011, 11(3), 381-389. Available at SSRN: https://ssrn.com/abstract=1323252 or http://dx.doi.org/10.2139/ssrn.1323252

Aleš Černý (Contact Author)

Cass Business School, City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Ioannis Kyriakou

City University London - Sir John Cass Business School ( email )

Faculty of Actuarial Science & Insurance
106 Bunhill Row
London, EC1Y 8TZ
United Kingdom
+44 (0)20 7040 8738 (Phone)
+44 (0)20 7040 8881 (Fax)

HOME PAGE: http://www.cass.city.ac.uk/experts/I.Kyriakou

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