An improved convolution algorithm for discretely sampled Asian options

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. (2008), and, if we restrict our attention only to lognormally distributed returns, also Veµ ceµ r (2002). While the existing convolution algorithms compute the density of the underlying state variable by moving forward on a suitably de…ned state space grid our new algorithm uses backward price convolution, which resembles classical lattice pricing algorithms. For the …rst 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 bene…ts of the new scheme and benchmark its performance against existing …nite di¤erence, Monte Carlo, and forward density convolution algorithms. Permanent repository link

Pricing of Discretely Sampled Asian Options Under Levy Processes

“…AsČerný and Kyriakou [27], we first reduce the pricing problem to a series of pricing of European options. However, the efficiency of an approach of this kind strongly depends on the type of the constructed sequence of European options, and the efficiency of the pricing the European options which inevitably have rather complicated payoffs.…”

“…Since the transition density function of a Lévy process is generally unknown in the closed form, the accuracy of this approach crucially rely on the accuracy on an approximation of the transition density function.Černý and Kyriakou [27] reduce the pricing problem to a sequence of European options in the one-factor model, and use trapezoidal rule as the numerical realization of the (inverse) Fourier transform to approximate the prices of European options. More recently, Chen et al [28,29] developed a Monte Carlo algorithm for simulating Lévy processes, based on calculation of the pdf using the Fourier inversion, and applied this algorithm to pricing discretely sampled Asian option.…”

“…This is due to the fact that the truncation error in the frequency domain is rather large. [27]. In this subsection , we compare the performance of our algorithm with the performance of the method developed byČerný and Kyriakou [27].…”

“…[27]. In this subsection , we compare the performance of our algorithm with the performance of the method developed byČerný and Kyriakou [27]. We use three parameter sets for KoBoL model (see (2.12)) considered in [27] Table 4.…”

“…The numerical parameters of our algorithm are specified in the caption to the table. (We use the acronym "LX" and "CK" to label the results obtained using our method and the method in [27], respectively.) We observe that the prices increase as m 2 increases as it is to be expected.…”