Efficient pricing of spread options with stochastic rates and stochastic volatility

Abstract

Spread options are notoriously difficult to price without the use of Monte Carlo simulation. Some strides have been made in recent years through the application of Fourier transform methods; however, to date, these methods have only been applied to specific underlying processes including two-factor geometric Brownian motion (gBm) and three-factor stochastic volatility models. In this paper, we derive the characteristic function for the two-asset Heston–Hull–White model with a full correlation matrix and apply the two-dimensional fast Fourier transform (FFT) method to price equity spread options. Our findings suggest that the FFT is up to 50 times faster than Monte Carlo and yields similar accuracy. Furthermore, stochastic interest rates can have a material impact on long-dated out-of-the-money spread options.