Matched Asymptotic Expansions for Valuing Spread Options

Abstract

Spread Options are crucial in the energy, currency and fixed income, and com-
modity markets. The problem with spread options is that there are no closed-
form formulae to price or hedge them. In this paper, we use matched asymptotic
expansions in order to price spread options. We use both one-factor and two-
factor models. In the one-factor models we assume the spread follows one of
the following processes: Geometric Brownian Motion, Ornstein-Uhlenbeck and
Arithmetic Brownian Motion. In the two-factor models, we assume the assets
follow one of these processes.