What it means
An ordinary option is linked to one asset, such as the shares of one company. A rainbow option is linked to several, and the name refers to the many "colours" of underlying assets.
Because it combines assets, the payout depends on how they move relative to one another as well as on how each one moves alone. The most common types are best-of and worst-of.
In a best-of call, the payout depends on the asset that performed best, so the buyer only needs one asset to do well. In a worst-of call, the payout depends on the asset that did worst, so all assets must perform for the buyer to be paid, which makes it cheaper.
Correlation is central to pricing. This is a measure of how closely the assets move together.
When assets are strongly linked, a best-of option is worth less, since the assets tend to rise and fall together, and a worst-of option is worth more. Rainbow options are traded over the counter, which means privately between two parties and not on an exchange.
They are used by investment banks, funds and corporate treasuries, and often sit inside structured products offered to investors. Because they are complex, the terms and pricing model should be understood before buying.
The main risks are model risk, because the pricing depends on estimated correlations that can change, and counterparty risk, which is the chance that the seller cannot pay. Liquidity can also be poor, since a bespoke contract may be hard to sell before maturity.
Finance teams should value these contracts carefully and disclose them appropriately in the accounts. Valuation usually relies on simulation, in which a computer generates thousands of possible price paths for all the assets together and averages the resulting payoffs.
This is called Monte Carlo simulation. The quality of the answer depends on the inputs, especially volatility and correlation, so independent price checks are common.
In practice
Real-world examples.
Example
A fund manager believes at least one of three technology shares will rise sharply, but cannot tell which one. She buys a best-of call on the basket. If any share performs strongly, the option pays out.
Example
A bank sells a structured note to retail clients that pays a coupon only if the worst of four indices stays above a set level. The embedded worst-of option makes the coupon higher than a plain note. Clients need to understand that one weak index can remove the coupon, even if the other three indices perform well.
Example
A corporate treasurer exposed to three commodities buys a rainbow option to hedge against the worst-performing price. The structure costs less than three separate options. The treasury team documents the hedge for the auditors.
Formula
Calculation
Best-of call payoff = notional x maximum of (best return among the assets - strike return, 0)
Suppose a fund buys a best-of call on three shares with a notional of $1,000,000 and a strike return of 0%. At expiry the returns are share A +12%, share B +5% and share C -3%.
Step 1: the best return is +12%.
Step 2: payoff = $1,000,000 x (12% - 0%) = $1,000,000 x 0.12 = $120,000.
For comparison, a worst-of call would use the worst return of -3%, so the payoff would be $0, because the maximum of (-3%, 0) is 0.Case study
Seen in the real world.
Prism Capital is a fictional investment firm used for illustration. Its portfolio manager wanted exposure to three emerging-market indices but was unsure which would lead. The bank suggested a best-of call with a $1,000,000 notional, priced at a premium of $45,000.
In this illustrative story, one index rose 12% while the others were flat or lower, so the option paid $120,000 and the net gain after the premium was $75,000. The risk team noted that the price had depended heavily on assumed correlation between the indices. After this, the firm built a routine for stress-testing correlation assumptions before buying such products.
The portfolio manager also learned that the dealer's quote for the same option moved noticeably when the assumed correlation changed by a few points. The risk committee asked for a one-page sensitivity table to accompany every future request. It also set a limit on the total premium the fund could spend on such products in a year.
Watch out
Common mistakes.
- Ignoring correlation. It is the key driver of the option's price and value.
- Confusing best-of with worst-of. Their payouts and risks are very different.
- Treating it like a simple option. The multi-asset structure adds complexity and model risk.
Questions
People also ask.
What is a rainbow option?
It is an option whose payout depends on two or more underlying assets.
Why is a worst-of option cheaper than a best-of option?
A worst-of option pays only if even the weakest asset performs, which is less likely, so its premium is lower.
Where are rainbow options traded?
They are mostly traded over the counter between banks and clients, and often appear inside structured products.
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