HISTORICAL VaR

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hao
Posts: 3
Joined: Sat Feb 13, 2010 5:43 pm

HISTORICAL VaR

Postby hao » Sat Feb 13, 2010 11:38 pm

Hi Carol,
In the IV3.3.3, you discussed how to adjust the historical return distribution by its Garch volatility weight. Then you compared the VaR result of unadjusted return and adjusted return. However, I am not sure how the calculation is proceeded because you did not state the detail of the calculation of Var.

VaR(h,?)=?^?1(1??)?h ??h (IV 1.15)

the above is the formula to calculate VaR. Since ? is given, ?(expected return) is also subjectively chosen, ? is estimate by Garch at time h, so why we still need to adjust the return distribution? Because adjusting the return does not change the inputs, am I right?

If I am wrong(may due to the IV1.15 is only appropriate when we assume normal distribution) , can you tell me how the VaR is calculated in the volatility adjusting case( or how the percentile is calculated)? Thanks

Because I just start to learn VAR, my question tends to be stupid to professionals. I apologize for it. Thanks for your reply.

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

Re: HISTORICAL VaR

Postby coalexander » Sun Feb 14, 2010 10:41 pm

Hi Hao

The VaR is calculated using historical simulation: see p160, penultimate paragraph, Ex IV.3.1 which begins: [quote:3b7f5chg]We now calculate the volatility adjusted returns that form the basis of the empirical distribution from which the historical VaR is computed as a quantile.[/quote:3b7f5chg]

The formula you gave, with the sigma being the GARCH vol is not actually correct under any circumstances, with or without volatility adjustment: it only applies when you assume the returns are normal, and independent, with constant volatility. I am sure these things will become clearer in time, especially if you go through the books slowly, and take care to look carefully through all the examples.

Please - no need for apologies `:oops:` - I am happy to offer a personal service to my readers, and this question has allowed me to emphasize how much I recommend volatility adjustment: indeed, without this, historical VaR models would still be producing excessively high VaR estimates now, even though the banking crisis appears to be behind us

Warm wishes, Carol
Last edited by coalexander on Sun Feb 14, 2010 10:44 pm, edited 1 time in total.
Reason: ??Swhç

hao
Posts: 3
Joined: Sat Feb 13, 2010 5:43 pm

Re: HISTORICAL VaR

Postby hao » Mon Feb 15, 2010 10:36 am

Hi Carol,

Thank you very much. I will keep working on it.


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