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
Options spreads are the basic building blocks of many options trading strategies. A spread position is entered by buying and selling options of the same class on the same underlying security but with different strike prices or expiration dates. A ...
'. A spread option is a new, relatively rare type of
exotic option
In finance, an exotic option is an option which has features making it more complex than commonly traded vanilla options. Like the more general exotic derivatives they may have several triggers relating to determination of payoff. An exotic op ...
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
In mathematical finance, Margrabe's formula is an option pricing formula applicable to an option to exchange one risky asset for another risky asset at maturity. It was derived by William Margrabe (PhD Chicago) in 1978. Margrabe's paper has been ...
, 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, 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. Kirk's approximation can also be derived explicitly from
Margrabe's formula
In mathematical finance, Margrabe's formula is an option pricing formula applicable to an option to exchange one risky asset for another risky asset at maturity. It was derived by William Margrabe (PhD Chicago) in 1978. Margrabe's paper has been ...
.
The same year Pearson published an algorithm
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, Choi (2018) showed that the numerical integral can be done very efficiently.
Li, Deng, and Zhou (2006) published accurate approximation formulas for both spread option prices and their Greeks.
See also
* Rainbow option Rainbow option is a derivative exposed to two or more sources of uncertainty, as opposed to a simple option that is exposed to one source of uncertainty, such as the price of underlying asset.
The name of ''rainbow'' comes from Rubinstein (1991), ...
References
Options (finance)
Derivatives (finance)
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