An improved convolution algorithm for discretely sampled Asian options

Černý, A. & Kyriakou, I. (2010). An improved convolution algorithm for discretely sampled Asian options. Quantitative Finance, 11(3), pp. 381-389. doi: 10.1080/14697680903397667

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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 [Risk, 1990, 3(4), 25–29], Benhamou [J. Comput. Finance, 2002, 6(1), 49–68], and Fusai and Meucci [J. Bank. Finance, 2008, 32(10), 2076–2088], and, if we restrict our attention only to log-normally distributed returns, also Večeř [Risk, 2002, 15(6), 113–116]. 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.

Item Type: Article
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Quantitative Finance on 20/4/2010, available online: http://wwww.tandfonline.com/10.1080/14697680903397667.
Uncontrolled Keywords: Asset pricing; Incomplete markets; Performance evaluation; Path-dependent options
Subjects: H Social Sciences > HG Finance
Divisions: Cass Business School > Faculty of Finance
URI: http://openaccess.city.ac.uk/id/eprint/12180

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