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.[1][2]

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 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,[3] 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[4] requiring a one-dimensional numerical integration to compute the option value. Used with an appropriate rotation of the domain and Gauss-Hermite quadrature, Choi (2018)[5] showed that the numerical integral can be done very efficiently.

Li, Deng and Zhou (2006)[6] published accurate approximation formulas for both spread option prices and their Greeks.

See also

Rainbow option

References

  1. ↑ Global Derivatives: Spread option
  2. ↑ Investopedia:Spread option
  3. ↑ Kirk E. (1995); Correlation in the Energy Markets, in: Managing Energy Price Risk, Risk Publications and Enron, London, pp. 71–78
  4. ↑ N. Pearson: An efficient approach for pricing spread options
  5. ↑ Choi, J (2018). "Sum of all Black-Scholes-Merton models: An efficient pricing method for spread, basket, and Asian options". Journal of Futures Markets. 38 (6): 727–644. arXiv:1805.03172. doi:10.1002/fut.21909. SSRN 2913048.
  6. ↑ Li, Deng and Zhou: Closed-Form Approximations for Spread Option Prices and Greeks


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