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. I use the following data(http://uploadeasy.net/upload/cdm3n.rar) which are 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") #add VaR 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]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
-- Patrick Burns pbu...@pburns.seanet.com twitter: @burnsstat @portfolioprobe http://www.portfolioprobe.com/blog http://www.burns-stat.com (home of: 'Impatient R' 'The R Inferno' 'Tao Te Programming') ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
