Valuation of spread options using the fast Fourier transform under stochastic volatility and jump diffusion models

Abstract: Spread options have become very popular in basically every sector of the financial markets, although the pricing of these derivatives still remains a challenge. In this thesis we examine the pricing of spread options using the fast Fourier transform (FFT). We implement a FFT method derived by Hurd and Zhou [10] and investigate the performance of the method under three different market models: the 2-asset geometric Brownian motion framework, a stochastic volatility model and a stochastic volatility model including random jumps in the asset dynamics. The third model is essentially a multivariate extension of Bates model where the jumps are distributed according to a compound Poisson process with log-normally distributed jump sizes. In doing so we successfully extend the work of Hurd and Zhou to include random jumps in the asset dynamics. The choice of models is motivated by the diverse applications of the spread options and its widespread usage in the energy markets. In addition to showing that the method produces accurate prices at an attractive computational expense, we provide valuable information regarding how to specify the parameters inherent in the method, which is well needed for implementation. Lastly we look at the price sensitivity to the various market parameters which is considered fundamental for the understanding of the model and can have implications for both the calibration problem and trading.