How Correlation Affects Basket Autocallable Values and Greeks

# Impact of correlation on greeks of a multi-underlying autocallable product


# Impact of correlation on greeks of a multi-underlying autocallable product












Please could someone explain how the greeks (especially the delta) of a multi-underlying autocallable product (i.e. an autocall on a basket) change when the correlation of the underlyings fluctuates?

Thanks

## Answer by Arshdeep (score 1)

https://quant.stackexchange.com/a/79661

Just think of the basket as a single thing. Correlation affects vol of this. So the effect is, correlation up, vol up, autocall probability higher, product more valuable. So delta is higher as vol goes up. This is for the linear basket.

About the forward, I am looking at the link of AKdemy. If basket is not linear, So the underlying is

$Max(X,Y,Z)$

which is obviously non linear so it's value depends on volatility. If X,Y,Z are determinitstic with $E(X)=E(Y)=E(Z)=0.5$ then the expectation is $0.5$. Now let's make $X$ and $Y$ I.I.D binomial. So the $E(max)$ is $0.875$. If $X$ and $Y$ are perfectly correlated then $E(max)$ is $0.75$. So correlation decreases the forward. This can also affect delta as the autocall probability is now lower.

Basically you want to put as many different things as possible in the $max$ to make it as much as possible. If those things are correlated (so put the same item again and again) it does not benefit.

If you are giving an exam and your instructor wants to award you the best of 100 attempts, would you want luck to play a part in your attempts - Would you want the attempts to be decorrelated?

## Answer by AKdemy (score 0)

https://quant.stackexchange.com/a/64190

The impact will be uncertain as stated here 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

Now, point 1 is in itself not 100% clear if you price with stochastic vol models that exhibit a so decorrelation effect. Since SV has vols fluctuate as opposed to deterministic, you get more variation in the price of the underlyings. Hence, your effective realized correlation is smaller in SV. Even that is not the end of the story because Autocallables are short volatility, so when Vol is reduced the price goes up (all else equal). This effect is called bi-locality. The paper I linked demonstrates that for large vol-vol correlation, the bi-locality effect is the one that dominates. In the absence of correlation between the variances, decorrelation dominates.

In terms of what the greeks look like in general, that is in itself quite difficult to answer for various reasons. Greeks will be bump and reprice, with all the complications and implementation choices. Ignoring these, it still remains difficult to answer as there is a number of factors affecting this. You can find simple and intuitive charts here.