Pricing two-asset rainbow options with the fast Fourier transform

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.