Pricing two-asset rainbow options with the fast Fourier transform
Loading...
Date
Authors
Levendis, Alexis Jacques
Mare, Eben
Journal Title
Journal ISSN
Volume Title
Publisher
South African Statistical Association (SASA)
Abstract
In this paper, we present a numerical method based on the fast Fourier transform
(FFT) to price call options on the minimum of two assets, otherwise known as
two-asset rainbow options. We consider two stochastic processes for the underlying
assets: two-factor geometric Brownian motion and three-factor stochastic volatility.
We show that the FFT can achieve a certain level of convergence by carefully choosing
the number of terms and truncation width in the FFT algorithm. Furthermore,
the FFT converges at an exponential rate and the pricing results are closely aligned
with the results obtained from a Monte Carlo simulation for complex models that
incorporate stochastic volatility.
Description
Keywords
Characteristic function, Rainbow option, Three-factor stochastic volatility, Two-factor geometric Brownian motion, Fast Fourier transform (FFT)
Sustainable Development Goals
None
Citation
Levendis, A. & Mare, E. 2023, 'Pricing two-asset rainbow options with the fast Fourier transform', South African Statistical Journal, vol. 57, no. 1, pp. 13-25. https://DOI.org/10.37920/sasj.2023.57.1.2.