# 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?

• See my comment in zrh's answer. – will May 4 '19 at 16:50

## 1 Answer

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

• This is wrong. If the basket has some optional it in it, ie a worst of/best of, which a rainbow basket can be described as, then the correlation does have an impact on the forward. – will Mar 16 '19 at 13:19
• ok, can you point us to a reference ? – ZRH Mar 16 '19 at 13:40
• i don't have one no. It's pretty obvious though, given the example in the question (50% best, 30% 2nd best, 20% worst), we can write it as a $0.9 \cdot \mathrm{equal weighted basket} + 0.2 \cdot \mathrm{best of} - 0.1 \mathrm{worst of}$. So correlation has no effect on the first term, but the min/max are effected by correlation (you can see the distributions here). – will Mar 17 '19 at 14:20