Rainbow And Best-Of Options

Imagine placing a bet before a race where you don't have to pick a horse in advance — you're simply paid based on whichever horse happens to win, no matter which one it is. That's the appeal of a best-of option: rather than betting on one specific stock's return, the holder gets the return of whichever stock in a chosen group did best, decided after the fact. "Rainbow" is the umbrella term for any option whose payoff depends on more than one underlying combined by some rule other than a simple weighted sum — best-of, worst-of, and "outperformance" options are all rainbows; a best-of call is the most investor-friendly member of the family.

The payoff

A best-of call on $n$ assets, struck at $K$, pays:

$$\text{Payoff} = \max\!\Big(\max(S_1(T), S_2(T), \dots, S_n(T)) - K,\ 0\Big).$$

In words: $S_1(T), \dots, S_n(T)$ are the expiry prices of each asset in the group, $\max(S_1(T),\dots,S_n(T))$ picks out whichever one ended up highest, and that best performer's price is compared against strike $K$ just like an ordinary call. The holder gets the payoff associated with the single best-performing asset in the group — never worse than betting on any one asset alone, and often better, because the "best of" selection happens with perfect hindsight after all the prices are already known.

Worked example 1 — picking the winner after the fact

A best-of call on three tech stocks (A, B, C), all struck at $100, expiry prices: A = $95, B = $130, C = $110. The max is B at $130. Payoff $= \max(130-100,0)=$ $30. A plain call on A alone would have paid $0 (A fell); on C alone, $10. The best-of structure automatically captured the outcome of whichever stock actually won, without the buyer having to guess in advance which of the three would be the strongest performer — that flexibility is exactly what the premium pays for.

Worked example 2 — why correlation makes it cheaper

Lower correlation between the underlyings makes a best-of option more valuable, not less — the opposite of what happens with a basket option. With three stocks that move almost independently (low correlation), there's a good chance at least one of them has a strong quarter even if the "market" overall is flat, so the max of the three tends to be meaningfully higher than any single stock's typical outcome. If instead the three stocks are near-perfectly correlated (they're really just one factor wearing three tickers), the max of three highly correlated draws barely beats a single draw — there's little extra value in "choosing the best," because they mostly move together anyway. Concretely: with correlation near 0, historical data might show the max of three uncorrelated 20%-vol stocks averaging noticeably above any one stock's own average return; with correlation near 1, that gap nearly vanishes.

Drag the correlation slider toward zero and picture picking the highest point in each vertical slice of the scatter — the more scattered the cloud (low correlation), the higher that running "best of" tends to sit above any single series' own average. Push correlation toward 1 and the cloud collapses onto a line, where picking the best of several nearly-identical series barely beats picking just one.

What this means in practice

Best-of options are attractive to investors who believe in a sector or theme but don't want to bet on which single name within it wins — a basket of AI stocks, say, where the buyer wants exposure to "whichever one runs" rather than a specific pick. They're structurally more expensive than a basket option on the same names, because "the best of several" is by construction at least as good as, and usually better than, any weighted average of the same group. Pricing requires modeling the full joint distribution of the underlyings, typically via Monte Carlo, since the max operator doesn't reduce to a clean closed form once there are more than two assets.