Spread Options as Compound Exchange Options with Applications to American Crack Spreads

This paper presents a new analytic approximation for pricing and hedging European and American spread options where the spread option price is represented as the price of an exchange option on two in-the-money European call options on the assets. We also extend the formula stated by Kirk [1996] to obtain approximate prices of American spread options on commodities and equity indices. However the new exchange option approach has many advantages over other approximations that are illustrated via simulations and by comparing the model's pricing and hedging performance using recent data on American crack spread options. Finally, the compound exchange option approximation is based on two correlated geometric Brownian motion price processes and this assumption has a straightforward extention to local volatility functions and local correlation. In this case it captures the volatility smiles in market prices of options on each underlying asset as well as the correlation `frown' that is observed in market prices of spread options.