Estimating Value-at-Risk using GARCH(1,1)

[sonja509]

Hello everybody!

I'm actually writing my Master's thesis right now and got stuck on a (I think not too complicated problem) which I just can't figure out.

What I want to do is to estimate the Value-At-Risk, given a time series of the German Stock Index DAX for a time horizon of 10 years.

With the Variance-Covariane-Method it already worked and I just this formula:

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series var var = @mean(log_returns) + @qnorm(0.05)*@stdev(log_returns)

Now, I want to estimate the VaR using a GARCH(1,1) process for the volatility
I tried this:

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series vargarch equation eq1.arch(1,1) log_returns c eq1.makegarch cvar_log_returns vargarch = @mean(log_returns) + @qnorm(0.05)* @sqrt(cvar_log_returns)

but this just gives me a series for the VaR with all different values. What I'm looking for is ONE value-at-Risk value for all of the time period.

I would really appreciate your help! Thanks in advance!
Sonja

[sonja509]

So I'm not sure if I was clear - and probably delcaring the VAR as a series is wrong anyways since I only want one number!

I'm looking for the conditional standard variation of a time series using GARCH(1,1). What I am getting with the formula below is a time series with a standard deviation value for each day.

But I just want one value for all the historical data (which is 10 years).


Would be so grateful for help!!!!
Thanks
Sonja

[trubador]

I am not sure, but you may be missing the point in VaR calculation. GARCH estimation on historical data will give you a time varying variance structure, so you should expect to have a standard deviation value for each day. As far as I know, you should then use this model to forecast both the return and variance for h-step to obtain the corresponding VaR for h-day horizon, which would be the single number you are seeking.

[sonja509]

Ok, but if I use the mean and the estimated standard deviation for each day of the time series, I will get a VaR number as well for each day of the time series.

What I need though is the 1-day value-at-risk value for a confidence level of e.g. 95% for the whole time horizon of the historical data.

How is it that I can obtain this number?

[trubador]

That is exactly what h-step forecasting means. In your case, after you estimate your model with the historical data (t=1,2,....,T), you can forecast the T+1 values of mean and variance and calculate VaR. I think what really confuses you is the changing variance. However, the most important outcome of GARCH estimation is the conditional variance, which is time varying. GARCH approach is quite different than Variance-Covariance method, where you calculate a fixed standard deviation based on entire historical data. The beauty of GARCH method is that it gives you the power of forecasting the variance as well.

I believe you are having some difficulties regarding the theoretical foundations of VaR calculation or maybe I misunderstand the question. But I am sure that there isn't any problem regarding EViews in your case.

[M.Nourani]

What Trubador is saying is right. you are misunderstood with the GARCH value-at-Risk concept. I did my master project in VaR and CVaR using different methods. ARCH, GARCH, EGARCH, ... . The beauty of GARCH is that the Variances for each day is the function of previous day. If you are looking for a 1-day VaR, you definitely have to specify your day, like Normal Linear or Historical Simulation methods. Let's say first Jan 2012. In your GARCH VaR series, if you are looking for 1-day for your comparison, choose the first Jan 2012.
In other cases, you can have an average of GARCH VaR for your selected period. This could be called average of 1-day GARCH VaR for let's say 10 years.

[rwb9227]

Hi, I am very new to Eviews, but I am also trying to calculate VaR of just a single equity. Currently I have generate the series of log returns and want to know how to calculate parametric VaR for say the first 100 observations then the first 101 then 102 etc, so I can plot the change over time, not forecasting just yet. Can anyone please explain how to do this? It would be of great help