ABSTRACT
Commodity spreads are important for both investors and manufacturers. For example, the price spread between heating oil and crude oil (crack spread) represents the value of production (including profit) for a refinery firm. If an oil refinery in Singapore can deliver its oil both to the US and the UK, then it possesses a real option of diversion which directly relates to the spread of WTI and Brent crude oil prices. ere are four commonly used spreads: spreads between prices of the same commodity at two dierent locations (location spreads) or times (calendar spreads), between the prices of inputs and outputs (production spreads) or between the prices of dierent grades of the same commodity (quality spreads).*
A spread option is an option written on the dierence (spread) of two underlying asset prices S1 and S2, respectively. We consider European options with payoff the greater or lesser of S2(T)–S1(T)–K and 0 at maturity T for strike price K and focus on spreads in the commodity (especially energy) markets (for both spot and futures). In pricing spread options it is natural to model the spread by modelling each asset price separately. Margrabe (1978) was the first to treat spread options and gave an analytical solution for strike price zero (the exchange option). Closed form valuation of a spread option is not available if the two underlying prices follow geometric Brownian motions (see Eydeland and Geman, 1998). Hence various numerical techniques have been proposed to price spread options, such as for example the Dempster and Hong (2000) fast Fourier transformation approach. Carmona and Durrleman (2003) oer a good review of spread option pricing.
