Pricing of spread options in energy markets

Abstract

The objective of this thesis is to value spread options with payoff function on the form max(S_1(T)-hS_2(T)-K,0), where S_1(T) and S_2(T) are the spot prices of two energy commodities at maturity time T, h is the heatrate and K is the strike price. We model (X_1(t),X_2(t))=(log(S_1(t)),log(S_2(t)) as a bivariate Ornstein-Uhlenbeck Lévy process. First, we consider an Ornstein-Uhlenbeck process driven by a bivariate Brownian motion, then we extend the model to an Ornstein-Uhlenbeck process driven by a bivariate Lévy process with jumps. We compute the characteristic function of (X_1(t),X_2(t)) in both models, and study the stationary properties of the distribution of (X_1(t),X_2(t)). Then we we derive a closed form formula for the option price in the continuous model for the case K=0. In the model with jumps, we use a Fourier transform method to express the price as an integral of the characteristic function of (X_1(T),X_2(T)) times the Fourier transform of the payoff function. When K!=0, we use a first order Taylor-expansion to approximate the option price. We find a closed form formula for the approximated price in the continuous model, and use simulations to check how good the approximation is for different values of K and for different values of the correlation between the two underlying price processes.