How Correlation Affects Rainbow Option Prices and Basket Forwards

Summary

The document asks why greater correlation might lower the forward value of a basket used in a rainbow option, where the basket payoff weights stocks according to their ranking. It presents two proposed effects: correlation may raise basket volatility and thereby support the option price, while a lower forward might work in the opposite direction.

The sole answer rejects the second effect, stating that correlation does not change the basket’s expected return and affects only its variance. This is a concise conceptual correction, not a derivation or a pricing analysis. It gives no assumptions about the constituent assets, payoff details beyond an illustrative ranking-based basket, or evidence beyond the assertion. The volatility channel is mentioned but not developed, so the note does not establish the net effect of correlation on a particular rainbow option’s price.

Key ideas

• The question concerns correlation sensitivity for an option on a ranking-weighted basket.
• The proposed volatility effect is that higher correlation can increase basket variance and potentially raise option value.
• The answer says correlation alone does not change the basket’s expected return or forward value.
• The document does not derive a general price sensitivity for specific rainbow payoffs or asset assumptions.

Tags

# Correlation sensitivity of Rainbow options


# Correlation sensitivity of Rainbow options












I read from various sources (eg. Exotic Options and Hybrids, M. Bouzoubaa) that the correlation sensitivity of Rainbow options (say a call price on a basket made of 50% of the best stock, 20% of the worst, 30% of the 3rd one) is uncertain due to 2 opposite effects:

- Increasing correlation would increase the overall basket volatility, thus tends to push the option price higher

- Increasing correlation would decrease the Forward price, thus tends to push the option price lower

I do not understand the reason for the 2nd point - how come an increase in correlation decreases the Forward price?

## Answer by ZRH (score -1)

https://quant.stackexchange.com/a/44048

The second point is obviously wrong. Correlations do nothing to the expected basket return, they will only affect the variance of the basket return.

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