Spread option


In finance, a spread option is a type of option where the payoff is based on the difference in price between two underlying assets. For example, the two assets could be crude oil and heating oil; trading such an option might be of interest to oil refineries, whose profits are a function of the difference between these two prices. Spread options are generally traded over the counter, rather than on exchange.
A 'spread option' is not the same as an 'option spread'. A spread option is a new, relatively rare type of exotic option on two underlyings, while an option spread is a combination trade: the purchase of one option and the sale of another option on the same underlying.

Spread option valuation

For a spread call, the payoff can be written as where S1 and S2 are the prices of the two assets and K is a constant called the strike price. For a spread put it is.
When K equals zero a spread option is the same as an option to exchange one asset for another. An explicit solution, Margrabe's formula, is available in this case.
In 1995 Kirk's Approximation, a formula valid when K is small but non-zero, was published. This amounts to a modification of the standard Black-Scholes formula, with a special expression for the sigma to be used, which is based on the volatilities and the correlation of the two assets.
The same year Pearson published an algorithm requiring a one-dimensional numerical integration to compute the option value. Used with an appropriate rotation of the domain and Gauss-Hermite quadrature, Choi showed that the numerical integral can be done very efficiently.
Li, Deng and Zhou published accurate approximation formulas for both spread option prices and their Greeks.