Why Basket Calls Have Positive Correlation Exposure

Summary

The document explains why a call option on a basket of stocks is commonly described as having positive exposure to correlation. A basket’s value depends on the combined returns of its constituents, so its distribution is more complicated than the distribution of a call on a single stock. In a Black-Scholes setting, the basket is modeled as a sum of lognormal asset prices, whose exact distribution is not specified by the standard single-asset formula.

The response uses the variance of that sum to motivate the intuition: holding constituent volatilities fixed, increasing their correlations raises the variance of the basket. This parallels the usual idea that a single-stock call benefits from higher volatility, making positive correlation exposure plausible for a basket call. The explanation is explicitly an intuition, not a proof. It does not derive the option’s sensitivity to correlation or address effects from strike, weights, dividend assumptions, or changes in individual volatilities, so it should not be treated as a complete pricing argument.

Key ideas

• A basket call depends on the joint behavior of its underlying assets.
• In the Black-Scholes setting, a basket can be represented as a sum of lognormal asset prices.
• The variance of that sum increases when constituent correlation rises, with volatilities held fixed.
• Higher basket variance motivates the intuition that a basket call is long correlation.
• The variance argument makes the claim plausible but does not prove the option’s correlation sensitivity.

Tags

# Why is the holder of a basket call long correlation?


# Why is the holder of a basket call long correlation?












I'm told that the holder of a basket call is long correlation.

I understand that an increase in correlation leads to an variance of a portfolio.

But with one "degree of freedom" (high positive correlation), if one asset falls, so do the others. And with multiple degrees of freedom (correlation near zero), if one falls, the others may rise and bring the average into the money.

Is this reasoning wrong?

## Answer by Richi Wa (score 1)

https://quant.stackexchange.com/a/39457

If I have an option on one stock then I am long implied volatility -> we can easily show this.

For a portfolios of stocks (the basket) the underlying turns out to be the sum of lognormals in the Black-Scholes setting. We don't know the true distribution. But we can write down the variance of the sum which is a function that increases if volatilies increase or if the correlation increases.

Thus we are long correlation for similar reasons as in the one stock call sense. This is not a proof but at least it makes the statement plausible.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.