# [R] Value at Risk using a volatility model?

Patrick Burns pburns at pburns.seanet.com
Sun Apr 7 10:03:11 CEST 2013

```There is an example of using the t distribution
for VaR in:

http://www.portfolioprobe.com/2012/11/19/the-estimation-of-value-at-risk-and-expected-shortfall/

The trick is to know what the variance of the
distribution is for a given value of the degrees
of freedom.

Pat

On 06/04/2013 10:54, Stat Tistician wrote:
> Hi,
> I want to calculate the Value at Risk with using some distirbutions and a
> volatility model.
> losses (negative returns) of a company of approx. the last 10 years. So I
> want to calculated the Value at Risk, this is nothing else than the
> quantile. Since I have losses I consider the right tail of the distribution.
>
> Consider a first simple example, I assume the returns to follow a normal
> distribution with mean zero and a volatility, which is estimated for each
> day with a volatility model. Let's use a simple volatility model: The
> empirical standard deviation of the last 10 days. So I calculate the
> standard deviation of the first ten days and this is my estimate for the
> 11th day and so on, until the end of my data. So I assume for each day a
> normal distribution with mean zero and a sigma estimated by the voaltility
> mdoel. So I use this estimated sigma to calculate the quantile, which gives
> me the Value at Risk. The code would be:
>
> volatility<-0
> quantile<-0
> for(i in 11:length(dat)){
> volatility[i]<-sd(dat[(i-10):(i-1)])
> }
>
> for(i in 1:length(dat)){
> quantile[i]<-qnorm(0.975,mean=0,sd=volatility[i])
> }
> # the first quantile value is the VaR for the 11th date
>
> #plot the volatility
> plot(c(1:length(volatility)),volatility,type="l")
>
> lines(quantile,type="l",col="red")
>
>
> So in this case I understand everything and I can implement this. But now
> comes my problem: I want to use a t-distribution with paramters mu, nu and
> beta or even a generalized hyperbolic distribution. So in this case, I
> don't know how to plug in the estimates for sigma, since there is no sigma
> in the paramters? How can I implement the volatility model and e.g. the
> generalized hyperbolic distribution in this case to calculate the Value at
> Risk?
>
> Thanks
>
> 	[[alternative HTML version deleted]]
>
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> and provide commented, minimal, self-contained, reproducible code.
>

--
Patrick Burns
pburns at pburns.seanet.com