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.
