A transform-based method for pricing Asian options under general two-dimensional models

Weinan Zhang and Pingping Zeng

Quantitative Finance, 2023, vol. 23, issue 11, 1677-1697

Abstract: We propose a unified transform-based method, which we call the extended double spiral (EDS) method, for pricing arithmetic Asian options under general two-dimensional (2D) models that nest regime-switching Lévy models, stochastic volatility (SV) models with Lévy jumps, and time-changed Lévy models. We first construct a new single backward induction in the state space that relaxes the restriction of the independent increments of the log-asset price. Second, we build an exact and explicit double backward induction in the Fourier space based on this single backward induction, a combination of the 1D Fourier transform method and a key function characterizing the 2D model, and the double spiral method. Third, we develop a unified EDS algorithm to recursively implement this double backward induction via the fast Fourier transform (FFT), various quadrature rules, asymmetric truncation boundaries, and so on. Extensive numerical results across a broad class of 2D models, monitoring frequencies, option moneyness, and model parameters demonstrate that our method is remarkably accurate, efficient, robust, simple to implement, and widely applicable.

Date: 2023
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DOI: 10.1080/14697688.2023.2256358

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