nikol


Total Posts: 1231 
Joined: Jun 2005 


Heston (or alike) applied for multiple assets, like basket of stocks, structurally embeds: A. assetvariance correlation (per asset, like it is in Heston or SABR) B. crossasset correlations (between returns of assets) C. crossvariance 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).
Questions: 1. Any suggestion how to measure or proxy crossvariance correlations (C.)? Intuitively, I guess that proxy could be linked to VIX level. Perhaps, can be extracted with some sort of VARMA with GARCHinnovations 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 crossvariance correlation (if I set it to zero)?




nikol


Total Posts: 1231 
Joined: Jun 2005 


clarified question (original was sloppy). still looking for opinion. 


ronin


Total Posts: 608 
Joined: May 2006 


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 


nikol


Total Posts: 1231 
Joined: Jun 2005 


@ronin
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/bestof feature, which I have, might give more sensitivity.



kloc


Total Posts: 40 
Joined: May 2017 


@nikol: you are right  in general there definitely can be significant volofvol sensitivity in structured products. However, the problem is that there's no liquid market of multiasset products to which you could calibrate crosscorrelations.
You can split the correlation matrix into 4 groups: (1) equityequity correlations which you are probably already estimating from historical price data, (2) diagonal equityvariance correlations which you fixed by calibrating Heston to vanillas (3) offdiagonal equityvariance correlations (stock 1 with variance 2 etc.), and (4) variancevariance 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 assetvariance offdiagonal 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 semidefinite. 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 crosscorrelations....




nikol


Total Posts: 1231 
Joined: Jun 2005 


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 stockstock corr, the incorporation of crossvols will be challenging. Hence, i wanted aside opinion whether it's worth the effort.
Yes, my stockstock corr is historical returnreturn 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 retret correlation should be corrected.


