Volatility Adjustment

Discussion on Value-at-Risk Models
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slava
Posts: 7
Joined: Thu May 05, 2011 3:02 pm

Volatility Adjustment

Postby slava » Tue May 24, 2011 3:05 pm

Hi Carol,
My another question is about Volatility Adjustment:
From my point of view it's useful to estimate the distribution form and correlation, but on the contrary it's harmful for short term volatility (it keeps place for mean reversion only), so it's not obvious if it makes sense to apply volatility weighting for historical VaR, especially for short term?
What do you think about this issue?
Thanks and regards,
Slava

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

Re: Volatility Adjustment

Postby coalexander » Mon May 30, 2011 11:22 am

I have quite a different view from you - its volatility adjustment more than correlation or functional form of distribution that matters most, especially for short term forecasting.

To put this in context, we are talking about historical simulation here (that is where the section on volatility adjustment is placed in Vol IV) where you need a very long series on each risk factor to get required accuracy in tail.

Market conditions change over time and currently you have the banking crisis in your sample, but now things are more calm and normal, your VaR will be as high as if the banking crisis happened yesterday, unless you adjust the vol.

The need for volatility adjustment is greater for short horizon forecasting - for a very long horizon say 1 year, it could indeed be that a crisis could occur again, so less need to adjust the historical sample to have similar volatility to today.

Also, the vol adjustment makes the sample much more like i.i.d. so sqrt of time rule is not so inappropriate as it is when you have vol clustering.

By contrast, correlation is too crude a metric to make much sense -- thats why most banks use historical simulation.

Cheers, Carol

slava
Posts: 7
Joined: Thu May 05, 2011 3:02 pm

Re: Volatility Adjustment

Postby slava » Mon May 30, 2011 1:28 pm

but if on the contrary: after a very long quite market, the crisis in just started – short term vol is exploded, but it happened too recently to significantly impact volatility normalisation – should we ignore incipient crisis for short term VaR..?

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

Re: Volatility Adjustment

Postby coalexander » Mon May 30, 2011 1:48 pm

I don't follow your reasoning, whole point is to use a time-varying volatility model for the filtering. Even simple expoential weighting (EWMA vol) reacts the day after the very large return...

slava
Posts: 7
Joined: Thu May 05, 2011 3:02 pm

Re: Volatility Adjustment

Postby slava » Wed Jun 01, 2011 9:19 am

appologies - my error...

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

Re: Volatility Adjustment

Postby coalexander » Thu Jul 14, 2011 10:57 pm

Indeed, there is a large literature in this area.

Trading time, as opposed to calendar time, spaces out time when volume of trading is low and speeds up time when trading volume is high.

The seminal work on this by Mark Yor -- published in the HEGY model see http://www.math.upatras.gr/dimitsana/th ... arcYor.pdf and http://en.wikipedia.org/wiki/Wiener_process#Time_change
and http://www.sciencedirect.com/science/ar ... 6605000336

But, all this is for the academic mathematical finance researchers, and you'll find more intuition about time-changed brownain motions from different soucres.

Emanuel Derman wrote a nice piece about 10 years ago, let me see if I can find it -- it think this it -- http://papers.ssrn.com/sol3/papers.cfm? ... _id=296401

Like most of Emanuel's stufff its a lot more accessible than the Madan-followers materials!

Cheers Carol

bhavnarpj
Posts: 1
Joined: Tue Jul 10, 2012 12:51 pm

Re: Volatility Adjustment

Postby bhavnarpj » Tue Jul 10, 2012 1:15 pm

Hi Carol,

I am using 2 years data (1105 daily observations) on an index and my observation is that the unadjusted returns give VaR higher than the volatility adjusted returns.
Just to make it clear, should I assume, that this is because of the crisis data, which is giving higher VaR for unadjusted returns?
Does the assumption that adjusted VaR is always better, change with different length of data?

Thanks,
Bhavna

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

Re: Volatility Adjustment

Postby coalexander » Wed Jul 11, 2012 9:39 am

Hi Bhavna

Do you mean 2 years (which is only about 500 daily observations) or really 1105 observations, which would have the banking crisis soon after the beginning of the sample?

To some extent it depends on what series you are examining: FX, Interest rates, equity, commodity? But on the whole there are especially volatile periods last quarter 2008 and also third quarter 2011.

Anyway, markets are a little more stable now than they have been in the past, so volatility adjusted VaR will be lower than unadjusted VaR because unadjusted VaR acts as if all the data are yesterday, including crisis periods.

Volatility adjustment becomes more important as data has more volatility clusters - and the large the sample usually the more volatility clusteres.

Hope this helps, Carol


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