Calculating Var for a Variance swap by proxying

Discussion of Pricing, hedging and Trading Financial Instruments
Forum rules
DISCLAIMER: We do not warrant or represent that this forum or its content is free of viruses, worms or other code that might be contaminating or destructive. We cannot guarantee that documents or files downloaded from the Site will be free from viruses and we do not accept any responsibility for any damage or loss caused by any virus. Accordingly, for your own protection, you must use virus-checking software when using the forum. You must not post or provide to us via the forum, any document or file which you believe may contain a virus. You must virus check any document or file which you intend to post or provide to us via the forum. You must ensure that any document or file you intend to post to the forum does not contravene any applicable laws or contravene any person's legal rights. We do not accept any responsibility for any damage or loss you may suffer.
GMS
Posts: 2
Joined: Tue Aug 14, 2012 7:21 pm

Calculating Var for a Variance swap by proxying

Postby GMS » Wed Aug 15, 2012 2:36 am

Suppose your risk analytics does not cover Variance Swaps and you decide to proxy it for example using a future on the related volatility index (e.g., VIX future with same maturity as the variance swap on VIX). How can you gauge the basis risk?
PS I understand that you can replicate the variance swap by a basket of options, but suppose you do not want to follow this path as it will be more operationally intensive. Thanks

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Calculating Var for a Variance swap by proxying

Postby coalexander » Wed Aug 15, 2012 8:38 am

Why not just use the VIX index itself as a proxy for the S\&P 500 variance swap rate (vsr)?

Then use data on s\&P 500 and VIX to compute variance risk premium (vrp) = difference between realised variance and vsr of same maturity as the swap.

If you are an issuing bank (paying realised) it is -vrp that you need to use measure VaR, otherwise just compute VaR from this vrp series. The vrp is typically small and negative, so issuing bank who pays realised usually makes a small profit. But vrp shoots upwards during volatile periods, and these banks can make enormous losses.

Using historical VaR can give very misleading picture because the risks on vrp are so highly sensitive to the market conditions. For issuing bank it is especially important to ensure your data includes banking crisis -- measure VaR using data from 1 Jan 2000 to 31 Dec 2009 and then use Jan 2010 -- now for backtesting, rolling the 10 year sample daily and computing 1-day VaR then doing usual coverage tests as described in Vol IV. Stress tests should always include banking crisis period, even if vrp has been small and neagtive for many years -- it can shoot up at any time without warning.

Hope this helps, Carol

PS Digression: There is a considerable difference between VIX and its futures. There is no trading on VIX, so no-arb doesn't apply and the `basis' VIX - VIX futures prices is very high and extremely variable. To measure variance of the variance swap rate, you'd need to use the S\&P indices (which are constant maturity VIX futures trackers representing investable returns) for the futures. They include a small roll cost which is almost always negative (when the futures term structure is in contango) but swings to be very high and positive at the onset of a crisis (when the term structure has a brief period of backwardation)

We have rtn VIX (y) = rtn S\&P Index (x) + rtn basis (e) where all rtns are daily log returns ln(P_t/P_{t-1}) for some price P

Then Variance operator V -> V(y) = V(x) + V(e) + 2Cov(x,e)

So if you use Variance of S&P indices of the same maturity as the variance swap on S\&P 500, ie using only V(x) instead of V(y), then you also need to add V(e) -- variance of returns on basis -- and Cov(x,e) which is definitely non-zero and probably high and positive (since 'basis' increases when volatility is high)

GMS
Posts: 2
Joined: Tue Aug 14, 2012 7:21 pm

Re: Calculating Var for a Variance swap by proxying

Postby GMS » Wed Aug 15, 2012 11:19 pm

Thank you very much for your reply. I have another question. Does anyone know how to map a vega notional of a Variance Swap to 1) the notional on VIX Future with same maturity; 2) notional exposure of VIX?

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Calculating Var for a Variance swap by proxying

Postby coalexander » Sun Aug 26, 2012 2:14 pm

The variance swap rate is based on VIX-type formula, and there is a very significant difference between statistical properties of VIX and VIX futures -- see my discussion paper on Diversification with VIX futures with Korovilas on ssrn or my webpage. So for this reason, no mapping is possible.

For mapping to VIX index, again I cannot see myself how a mapping would work, since vega exposure on variance swap is to the variance risk premium, i.e. difference between realised variance and implied variance not to the implied leg only (and VIX is just the implied leg).

Cheers, Carol


Return to “Volume III”

Who is online

Users browsing this forum: No registered users and 1 guest