An improved convolution algorithm for discretely sampled Asian options

Aleš Černý and Ioannis Kyriakou

Quantitative Finance, 2010, vol. 11, issue 3, 381-389

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 Vecer [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.

Keywords: Asset pricing; Incomplete markets; Performance evaluation; Path-dependent options (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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DOI: 10.1080/14697680903397667

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