1
$\begingroup$

From this document, http://quantlabs.net/academy/download/free_quant_instituitional_books_/[JP%20Morgan]%20Variance%20Swaps.pdf, on page 56, it states that

Losses from short correlation through variance dispersion can occasionally be very large, especially since the trade becomes short volatility following adverse moves in correlation.

I cannot see how short correlation through variance dispersion becomes short volatility.

$\endgroup$
  • $\begingroup$ You write "this document" but you didn't insert a link nor provided the name of the document you refer to. $\endgroup$ – LocalVolatility Mar 11 '17 at 19:50
  • 1
    $\begingroup$ It is JP Morgan's "Variance Swaps" in European Equity Derivatives Strategy from 17 Nov 2006. The entire issue is on variance swaps. $\endgroup$ – Alex C Mar 11 '17 at 20:08
2
$\begingroup$

Suppose you are short the index option, and long the single stock options (all vanillas). You size it in such a way that at inception you have flat vega, you hedge out all your deltas.

Now assume the market moves down. All your options move away from ATM and they all have less vega (both your long single stock options, as well as ur short index option).

OTM options are long vega convexity: when implied moves up, vega moves up. So while all your options lost vega due to moving away from the money. They will gain incremental vega due to a higher vol (assuming vol moves along the smile).

Index smile is steeper than single stock smile. So the index option - which you are short- gains more vegas relative to the single due to vega convexity. Combining it all, you are short vegas now. (both index and single lost vega due to spot move, but index lost less due to steeper smile).

$\endgroup$
  • 3
    $\begingroup$ In oversimplified terms, when the stock market crashes the correlation goes up, the index volatility (which you are short) goes up a lot and the individual stock volatilities (which you are long) go up only a little. $\endgroup$ – Alex C Mar 11 '17 at 20:13
  • $\begingroup$ It is not clear whether the options are initiated ATM, nor whether it is the single stock options or index option positions are OTM. Also I cannot see why given more or less smile why certain options would gain more vega (I know you stated vega convexity but I cannot see this) $\endgroup$ – Permian Mar 15 '17 at 19:16
  • $\begingroup$ if an option has positive vega convexity, it means that the vega is an increasing function of implied vol. So, the more the vol goes up the more your vega goes up. As Alex C also points out, if market crashes the correlations go up. So index vol goes up a lot more than single stock vol. Thus the short positon on the index will have more short vegas. $\endgroup$ – mbison Mar 16 '17 at 20:56

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.