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Total Posts: 1126
Joined: Jun 2005
Posted: 2020-06-28 16:15
Heston (or alike) applied for multiple assets, like basket of stocks, structurally embeds:
A. asset-variance correlation (per asset, like it is in Heston or SABR)
B. cross-asset correlations (between returns of assets)
C. cross-variance correlations, e.g. between IVOL or LVOL of assets. Of course not the entire surface/cube but, for example, correlation between ATM's vols at t=0 (at spot).

1. Any suggestion how to measure or proxy cross-variance correlations (C.)? Intuitively, I guess that proxy could be linked to VIX level. Perhaps, can be extracted with some sort of V-ARMA with GARCH-innovations applied to series of assets or similar animal. Or I could simply collect history of IVOL/LVOLs and measure what I want directly. What is easier not sure?

2. Is there any simple rule to quantify the neglect of cross-variance correlation (if I set it to zero)?


Total Posts: 1126
Joined: Jun 2005
Posted: 2020-06-30 12:36
clarified question (original was sloppy). still looking for opinion.


Total Posts: 585
Joined: May 2006
Posted: 2020-06-30 19:25
You shouldn't really care, should you? It really only affects things like options on baskets of variance swaps.

Just mark it to zero.

"There is a SIX am?" -- Arthur


Total Posts: 1126
Joined: Jun 2005
Posted: 2020-07-01 10:23

Basket of variance swaps has direct sensitivity via payoff, it's clear. But this is not my case (structured products). I am not so sure whether worst/best-of feature, which I have, might give more sensitivity.


Total Posts: 33
Joined: May 2017
Posted: 2020-07-01 14:25
@nikol: you are right - in general there definitely can be significant vol-of-vol sensitivity in structured products. However, the problem is that there's no liquid market of multiasset products to which you could calibrate cross-correlations.

You can split the correlation matrix into 4 groups:
(1) equity-equity correlations which you are probably already estimating from historical price data,
(2) diagonal equity-variance correlations which you fixed by calibrating Heston to vanillas
(3) off-diagonal equity-variance correlations (stock 1 with variance 2 etc.), and
(4) variance-variance correlations.
The problem is, therefore, to determine (3) and (4) and see what impact it has on the structured product you're dealing with.

I'm not sure about your specific goal, but, for pricing I would suggest to take an "investigative" approach and find conservative bounds. I would assume "flat correlations" for (3) and (4) separately: set all asset-variance off-diagonal correlations to be identical and set all variance correlations to be identical and find the allowed ranges for the two missing numbers which keep the overall correlation matrix positive semi-definite. This way you're not dealing with too many numbers (which you're anyways unable to determine) and you still have two free parameters with which you can investigate the impact of cross-correlations....


Total Posts: 1126
Joined: Jun 2005
Posted: 2020-07-01 15:15
My guts feeling is that
3) off diagonal is the smallest , while
4) can be significant by value and be close to 1 in cases when "global vol" (VIX) is high. but how large can it get? any clue?

The root of my question is that while I more or less easily incorporated stock-stock corr, the incorporation of cross-vols will be challenging. Hence, i wanted aside opinion whether it's worth the effort.

Yes, my stock-stock corr is historical return-return now, but I understand also that it's somewhat inconsistent with Heston or whatever model to be used. Corr(dSi, dSj) is not the same as Corr(dWi, dWj), but they are related, so the ret-ret correlation should be corrected.

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