Two-dimensional Shannon wavelet inverse Fourier technique for pricing European options

Abstract

The SWIFT method for pricing European-style options on one underlying asset was recently published and presented as an accurate, robust and highly efficient technique. The purpose of this paper is to extend the method to higher dimensions by pricing exotic option contracts, called rainbow options, whose payoff depends on multiple assets. The multidimensional extension inherits the properties of the one-dimensional method, being the exponential convergence one of them. Thanks to the nature of local Shannon wavelets basis, we do not need to rely on a-priori truncation of the integration range, we have an error bound estimate and we use fast Fourier transform (FFT) algorithms to speed up computations. We test the method for similar examples with state-of-the-art methods found in the literature, and we compare our results with analytical expressions when available.

A Shannon wavelet method for pricing foreign exchange options under the Heston multi-factor CIR model

“…This paper aims to further extend the applicabilities of these state-of-the-art numerical integration methods to the above-mentioned general jump-diffusion FX model. We use the SWIFT method, due to the established robustness of Shannon wavelets in option pricing, as demonstrated in a number of works, such as Colldeforns-Papiol et al (2017); Maree et al (2017); Ortiz-Gracia and Oosterlee (2016). The proposed SWIFT-based method is developed within the hybrid MC-PDE computational framework put forward in Dang et al (2015bDang et al ( , 2017.…”

SWIFT valuation of discretely monitored arithmetic Asian options

“…Then, the characteristic function is used to recover the series expansion coefficients of the density. SWIFT has already been successfully applied to European options with one and two underlying assets in [13] and [14] respectively, as well as to earlyexercise and discrete barrier options in [15]. It has been shown that among the strengths of SWIFT method is the a priori knowledge of the scale of approximation and equivalently the number of terms in the expansion.…”