Rainbow options - Introduction

What is a rainbow option

A rainbow option is an option linked to two or more underlying assets.

A rainbow is an option on a basket that pays in its most common form, a non- equally weighted average of the assets of the basket according to their performance.

The number of assets is called the number of colours of the rainbow. At maturity, the assets are sorted by their performance.

For instance, a rainbow call with weights 50%, 30%, 20%, with a basket including an equity stock index, a bond index and a foreign currency, pays 50% of the best return (at maturity) between the equity stock index, the bond index and the foreign currency, 30% of the second best and 20% of the third best.

A callable rainbow note allows the note issuer to call back the note while a putable one allows the note buyer to sell it back. Callable putable versions are becoming also common as they allow flexibility on both sides.

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 colours. More generally, rainbow options are multi- asset options, also referred to as correlation options. Rainbow can take various other forms but the combining idea is to have a payoff that is depending on the asset on the assets sorted by their performance at maturity.

How does it work

Just as rainbows have many colors, options can have many underlying assets. A Margrabe option, for example, gives the buyer the right but not the obligation to exchange one asset for another at a set price on or before the expiration date. Hence a Margrabe option is a rainbow option

In order for an option like this to make money for the investor, the price of the first asset and the price of the second asset both have to move in the desired direction to make exchanging one asset for another worthwhile. Because the option has "more than one color," we call Margrabe options rainbow options, though any option that derives its value from more than one asset is considered a rainbow option.

What are the complication involved

Rainbow options can be difficult to analyze because of their many moving parts, but the main idea is that all of the underlying assets in a rainbow option have to move in the "right" direction in order for the investment to pay off. Right direction does not mean in the same direction - for example if one has a right to exchange one asset for another then for the option to be valuable the price of one asset has to move up while the other asset has to move down.

Examples of Rainbow options

A rainbow option might allow the buyer to exchange 10 shares of ABC Ltd for one share of XYZ, which means they’d make money if ABC Ltd shares rose relative to IBM shares or ABC Ltd share remains constant while shares of XYZ Ltd moves down.

Rainbow options are most commonly used when valuing natural resources, since they depend on both the price of the natural resource and how much of the resource is available in a deposit. Traders use rainbow options to bet on both the price and quantity of a natural resource deposit before the option will take effect. Of course, the use of two variables makes these options riskier than traditional options.

Another example of a rainbow option is a basket option : An option contract in which the underlying asset consists of several different assets. For example, a basket call may give one the right, but not the obligation, to buy more than one currency at the strike price (which is denominated in a currency other than any in the underlying). A basket option provides a way for a corporation to hedge against several different risks at the same time and to do so more cheaply. However, a rainbow option is exposed to the risk that only some, rather than all, of the underlying assets will move in the direction benefiting the holder. A basket option is also called a rainbow option.

What is the reason for development of such a product:

Because of integration of various market, as a result of globalisation, speculators are now taking exposure across various class of assets. Moreover, options on many assets are appealing to investor for the following reasons:

Natural risk diversification.

A Rainbow option is often constructed by taking unrelated assets in a basket and therefore the performance of the basket will factor into account all movements across various class of assets.

Cost efficiency: Multi-asset products are cheaper than the corresponding sum of the individual options. The effect of correlation makes the product competitive.

Hedge against correlation. This may seem stupid statement, but correlation risk is very hard to risk manage and correlation products enable to lock up the implied correlation. Proper delta-hedging enables also to lock up the historical covariance.

Rainbow option offers the additional advantage to provide a weighed average on the best or worst performing assets. The best version supplies attractive returns, while the worst version is often very cheap option.

How are the options valued?

Valuing rainbow options are quite complicated - however one of the most common method used is the Black-Scholes model with certain modifications. The valuation is not discussed here - owing to its complexity it is separate topic for discussion by itself.

Note: This note is intended for students to have a basic knowledge about rainbow options and is not a detailed discussion paper. Valuation of such options is very complex and is hence not discussed here.

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