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 (vanilla) option and the sale of another option on the same underlying.

Spread option valuation

For a spread call, the payoff can be written as $C = \max(0,S_1-S_2-K)$ 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 $P = \max(0,K-S_1+S_2)$.

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 (volatility) 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 single numerical integration to compute the option value.

This method was improved upon in 2006 when Li, Deng and Zhou published accurate approximation formulas for both spread option prices and their Greeks.