# Spread option

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{{Short description|Financial derivatives trading strategy}}
{{for|the football offensive formation|Spread offense}}
In [finance](/source/finance), a '''spread option''' is a type of [option](/source/Option_(finance)) 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.<ref>[http://www.global-derivatives.com/index.php/component/content/46?task=view Global Derivatives: Spread option]</ref><ref>[http://www.investopedia.com/terms/s/spreadoption.asp#axzz1xK58zM00 Investopedia:Spread option]</ref>

A 'spread option' is not the same as an '[option spread](/source/Options_spread)'. A spread option is a new, relatively rare type of [exotic option](/source/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 <math>C = \max(0,S_1-S_2-K)</math> 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 <math>P = \max(0,K-S_1+S_2)</math>.

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](/source/Margrabe's_formula), is available in this case, and this type of option is also known as a Margrabe option or an outperformance option.

In 1995 Kirk's Approximation,<ref>Kirk E. (1995); Correlation in the Energy Markets, in: Managing Energy Price Risk, Risk Publications and Enron, London, pp. 71–78</ref> a formula valid when K is small but non-zero, was published. This amounts to a modification of the standard [Black–Scholes](/source/Black%E2%80%93Scholes_model) 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. Kirk's approximation can also be derived explicitly from [Margrabe's formula](/source/Margrabe's_formula).<ref>[https://ssrn.com/abstract=3665654 S.R. Etesami: Spread Options: From Margrabe to Kirk]</ref>

The same year Pearson published an algorithm<ref>[https://ssrn.com/abstract=7010 N. Pearson: An efficient approach for pricing spread options]</ref> requiring a one-dimensional numerical integration to compute the option value. Used with an appropriate rotation of the domain and [Gauss-Hermite quadrature](/source/Gauss-Hermite_quadrature), Choi (2018){{r|choi2018sumbsm}} showed that the numerical integral can be done very efficiently.

Li, Deng, and Zhou (2006){{r|li2008spread}} published accurate approximation formulas for both spread option prices and their Greeks.

==See also==
* [Rainbow option](/source/Rainbow_option)

==References==
{{Reflist|refs=
<ref name="choi2018sumbsm">
{{cite journal |last=Choi |first=J |title=Sum of all Black–Scholes–Merton models: An efficient pricing method for spread, basket, and Asian options |date=2018|journal=Journal of Futures Markets |volume=38 |issue=6 |pages=627–644 |doi=10.1002/fut.21909 |ssrn=2913048 |arxiv=1805.03172
|s2cid=59334133 |url=https://onlinelibrary.wiley.com/doi/abs/10.1002/fut.21909
}}</ref>
<ref name=li2008spread>
{{cite journal |last1=Li |first1=M |last2=Deng |first2=S-J |last3=Zhou |first3=J 
|title=Closed-Form Approximations for Spread Option Prices and Greeks
|journal=The Journal of Derivatives |year=2008 |volume=15 |issue=3 |pages=58–80 
|doi=10.3905/jod.2008.702506 |ssrn=952747
|s2cid=41872798 |url=https://jod.pm-research.com/content/15/3/58
|url-access=subscription }}</ref>
}}

{{Derivatives market}}

{{DEFAULTSORT:Spread Option}}
Category:Options (finance)
Category:Derivatives (finance)

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Adapted from the Wikipedia article [Spread option](https://en.wikipedia.org/wiki/Spread_option) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Spread_option?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.