SWIFT Valuation of Discretely Monitored Arithmetic Asian Options

Abstract

In this work, we propose an efficient and robust valuation of discretely monitored arithmetic Asian options based on Shannon wavelets. We employ the so-called SWIFT method, a Fourier inversion numerical technique with several important advantages with respect to the existing related methods. Particularly interesting is that SWIFT provides mechanisms to determine all the free-parameters in the method, based on a prescribed precision in the density approximation. The method is applied to two general classes of dynamics: exponential Lévy models and square-root diffusions. Through the numerical experiments, we show that SWIFT outperforms state-of-the-art methods in terms of accuracy and robustness, and shows an impressive speed in execution time.

Keywords: Arithmetic Asian options, Fourier transform, Shannon wavelets, SWIFT method, Exponential Lévy processes, Square-root diffusions, Option pricing

JEL Classification: C02, C60, C13