Rainbow option
Rainbow option
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Rainbow option

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Rainbow option

In finance, a Rainbow option is a derivative whose payoff depends on multiple underlying risky assets. Each underlying asset is referred to as a color of the rainbow. It contrasts with 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), who emphasises that this option was based on a combination of various assets like a rainbow is a combination of various colors.

When the rainbow only pays the best (or worst) performing asset, it is also called best-of (or worst-of). When the rainbow pays the weighted sum of the assets, it is a basket option. Other popular options that can be reformulated as a rainbow option are spread and exchange options.

Let be the prices of assets 1, 2, ..., n, and let be cash or cash equivalent.

In this formulation, some common rainbow options include:

Thus, the payoffs at expiry for rainbow European options are:

Rainbow options are usually calls or puts on the best or worst of n underlying assets. Like the basket option, which is written on a group of assets and pays out on a weighted-average gain on the basket as a whole, a rainbow option also considers a group of assets, but usually pays out on the level of one of them.

A simple example is a call rainbow option written on FTSE 100, Nikkei and S&P 500 which will pay out the difference between the strike price and the level of the index that has risen by the largest amount of the three.

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