[R-SIG-Finance] rugarch + VineCopula for value at risk
Ole Bueker
ole.bueker at outlook.com
Fri Aug 22 01:44:51 CEST 2014
Sorry for sending another message, but it seems like there is still an error in the formatting of the code..
I'll share the R code using dropbox, in case the code is still not readable in this email: https://www.dropbox.com/s/rc9kpanule52zu8/minimum_working.R
#Load data and define variablesreturns <- read.zoo("E:/Dropbox/my own/Programming/R/returns.csv", header=TRUE, sep=",", format="%d-%m-%y")model<-ugarchspec(variance.model=list(model="sGARCH",garchOrder=c(1,1)),mean.model=list(armaOrder=c(1,0),include.mean=FALSE),distribution.model="ged")times <- as.data.frame(time(returns_crisis))windows <- matrix(0, 20, 250)familyset <- c(1:5, 7, 10, 13, 14, 17, 20)sim <- array(0, dim = c(100, 20))residuals2 <- array(0, dim = c(100, 20))rvine_fitted <- array(0, dim = c(10,100,20))rvine_sigma <- array(0, dim = c(10,100,20))VaR01 = VaR05 = array(0, dim = c(10,100,20))
#Main calculationfor(i in 1:10){ print(i) windows <- window(returns_crisis[,1:20], start=times[376-250-24+i,1], end=times[376-25+i,1]) # Step 1 fit <- lapply(windows, ugarchfit, spec=model, solver="hybrid") print("rugarch fitting done")
residuals <- sapply(fit, residuals, standardize=TRUE) # Step 2 shape <- sapply(fit, coef) shape <- shape[5,]
UniformResiduals <- pged(residuals, nu = shape) # Step 3 if(any(UniformResiduals > 0.99999)) { ix = which(UniformResiduals > 0.99999) UniformResiduals [ix] = 0.99999 } if(any(UniformResiduals < .Machine$double.eps)) { ix = which(UniformResiduals < (1.5*.Machine$double.eps)) UniformResiduals [ix] = .Machine$double.eps } rvine <- RVineStructureSelect(UniformResiduals, indeptest=TRUE, familyset=familyset) # Step 4 print(paste(i,"RVine fitting done")) for(j in 1:100) { sim[j,] <- RVineSim(1, rvine) # Step 5 } print(paste(i,"RVine simulation done")) for(k in 1:20) { residuals2[,] <- qged(sim[,], nu = shape[k]) # Step 6
residuals_temp <- residuals2[,k] rvine_sim <- ugarchsim(fit[[k]], n.sim=1, m.sim=100, custom.dist = list(name=NA, distfit=residuals_temp)) # Step 7
rvine_fitted[i,,k] <- fitted(rvine_sim) # Step 8 rvine_sigma[i,,k] <- sigma(rvine_sim) if (i==10) { for(j in 1:100) { VaR01[,j,k] <- rvine_fitted[,j,k] + rvine_sigma[,j,k] * qdist('ged', 0.01, mu=0, sigma=1, shape = shape[k]) # Step 9 VaR05[,j,k] <- rvine_fitted[,j,k] + rvine_sigma[,j,k] * qdist('ged', 0.05, mu=0, sigma=1, shape = shape[k]) } }else {} } print(paste(i, "rugarch forecast done"))}
#Cleanupremove(i, j, k, ix, familyset, model, sim, rvine_sim, residuals, residuals_temp)
> From: ole.bueker at outlook.com
> To: alexios at 4dscape.com; r-sig-finance at r-project.org
> Date: Fri, 22 Aug 2014 01:10:55 +0200
> Subject: Re: [R-SIG-Finance] rugarch + VineCopula for value at risk
>
>
>
>
> I have no idea what happened to the formatting, looked fine to me when I typed it in Outlook.
> Here's the revised version, with amended code so that it is minimally reproducible (for this purpose, I will only use the first 25 companies, 100 simulations for 10 trading days).
> The revised code should take around 5 minutes,
>
>
> Again, heres the code summary:
> 1. Fit GARCH models to each series.
> 2. Extract standardized returns.
> 3. Transform standardized returns to uniform marginals using the parametric IFM method by Joe.
> 4. Fit vine copulas.
> 5. Generate 100 1-day ahead forecasts from the vine copulas.
> 6. Reverse transform the simulated values.
> 7. Use these transformed forecasts in ugarchsim (using custom.dist)
> 8. Extract forecasted mu and sigma.
> 9. Calculate 95% and 99% VaR.
>
> The full code:
> #Load data and define variablesreturns <- read.zoo("E:/Dropbox/my own/Programming/R/returns.csv", header=TRUE, sep=",", format="%d-%m-%y")
> model<-ugarchspec(variance.model=list(model="sGARCH",garchOrder=c(1,1)),mean.model=list(armaOrder=c(1,0),include.mean=FALSE),distribution.model="ged")times <- as.data.frame(time(returns_crisis))windows <- matrix(0, 20, 250)familyset <- c(1:5, 7, 10, 13, 14, 17, 20)sim <- array(0, dim = c(100, 20))residuals2 <- array(0, dim = c(100, 20))rvine_fitted <- array(0, dim = c(10,100,20))rvine_sigma <- array(0, dim = c(10,100,20))VaR01 = VaR05 = array(0, dim = c(10,100,20))
> #Main calculation
> for(i in 1:10){ print(i) windows <- window(returns_crisis[,1:20], start=times[376-250-24+i,1], end=times[376-25+i,1]) # Step 1 fit <- lapply(windows, ugarchfit, spec=model, solver="hybrid") print("rugarch fitting done")
> residuals <- sapply(fit, residuals, standardize=TRUE) # Step 2 shape <- sapply(fit, coef) shape <- shape[5,]
> UniformResiduals <- pged(residuals, nu = shape) # Step 3 if(any(UniformResiduals > 0.99999)) { ix = which(UniformResiduals > 0.99999) UniformResiduals [ix] = 0.99999 } if(any(UniformResiduals < .Machine$double.eps)) { ix = which(UniformResiduals < (1.5*.Machine$double.eps)) UniformResiduals [ix] = .Machine$double.eps } rvine <- RVineStructureSelect(UniformResiduals, indeptest=TRUE, familyset=familyset) # Step 4 print(paste(i,"RVine fitting done")) for(j in 1:100) { sim[j,] <- RVineSim(1, rvine) # Step 5 } print(paste(i,"RVine simulation done")) for(k in 1:20) { residuals2[,] <- qged(sim[,], nu = shape[k]) # Step 6
> residuals_temp <- residuals2[,k] rvine_sim <- ugarchsim(fit[[k]], n.sim=1, m.sim=100, custom.dist = list(name=NA, distfit=residuals_temp)) # Step 7
> rvine_fitted[i,,k] <- fitted(rvine_sim) # Step 8 rvine_sigma[i,,k] <- sigma(rvine_sim) if (i==10) { for(j in 1:100) { VaR01[,j,k] <- rvine_fitted[,j,k] + rvine_sigma[,j,k] * qdist('ged', 0.01, mu=0, sigma=1, shape = shape[k]) # Step 9 VaR05[,j,k] <- rvine_fitted[,j,k] + rvine_sigma[,j,k] * qdist('ged', 0.05, mu=0, sigma=1, shape = shape[k]) } }else {} } print(paste(i, "rugarch forecast done"))}
>
> #Cleanupremove(i, j, k, ix, familyset, model, sim, rvine_sim, residuals, residuals_temp)
>
> Hope this time everything is formatted correctly!
> After running the code, I export VaR01 and VaR05 to Excel, and notice that there's usually quite a few positive values.
> This seems to happen because sometimes the sigma is too low compare to the (positive) forecast, and therefore the VaR stays in the positive.
> My guess is that either there's a mistake in my code at step 3 (maybe the wrong shape is used?).Or more likely there's a mistake at step 6/7 (wrong transformation or transformed values are not inserted correctly into ugarchsim).
> > Date: Thu, 21 Aug 2014 18:21:49 +0100
> > From: alexios at 4dscape.com
> > To: ole.bueker at outlook.com; r-sig-finance at r-project.org
> > Subject: Re: [R-SIG-Finance] rugarch + VineCopula for value at risk
> >
> > Ole,
> >
> > The email you've sent is really badly formatted and all over the place.
> >
> > 1. Try to send a well structured text-only email (with no special
> > characters).
> > 2. Make an effort to send a minimally reproducible example.
> > Telling us that your problem took 8 hours to run is not the way to go.
> > Take a small subsample of your data which generates the behavior you
> > want to highlight (try to find one that does), and use that so that we
> > can investigate with minimal fuss.
> >
> > -Alexios
> >
> > On 21/08/2014 17:50, Ole Bueker wrote:
> > > Anyway, here�s my code so far:# Load Data and define variables
> > > returns <- read.zoo("E:/Dropbox/my own/Programming/R/returns.csv", header=TRUE, sep=",", format="%d-%m-%y")model<-ugarchspec(variance.model=list(model="sGARCH",garchOrder=c(1,1)),mean.model=list(armaOrder=c(1,0),include.mean=FALSE),distribution.model="ged")times <- as.data.frame(time(returns))windows <- matrix(0, 112, 250)familyset <- c(1:5, 7, 10, 13, 14, 17, 20) # The vine copulas to be testedsim <- array(0, dim = c(1000, 112))residuals2 <- array(0, dim = c(1000, 112))rvine_fitted <- array(0, dim = c(25,1000,112))rvine_sigma <- array(0, dim = c(25,1000,112))VaR01 = VaR05 = array(0, dim = c(25,1000,112))
> > >
> > > #Main calculation
> > > for(i in 1:25){ print(i) windows <- window(returns_crisis, start=times[376-250-24+i,1], end=times[376-25+i,1]) #Define the moving window fit <- lapply(windows, ugarchfit, spec=model, solver="hybrid") #Fit the garch models print("rugarch fitting done") residuals <- sapply(fit, residuals, standardize=TRUE) #Extract residuals & shape parameters shape <- sapply(fit, coef) shape <- shape[5,] UniformResiduals <- pged(residuals, nu = shape) #Transform residuals into uniform marginals if(any(UniformResiduals > 0.99999)) { ix = which(UniformResiduals > 0.99999) UniformResiduals [ix] = 0.99999 } if(any(UniformResiduals < .Machine$double.eps)) { ix = which(UniformResiduals < (1.5*.Machine$double.eps)) UniformResiduals [ix] =
> > .Machine$double.eps } rvine <- RVineStructureSelect(UniformResiduals, indeptest=TRUE, familyset=familyset) #Fit the Vine copulas print(paste(i,"RVine fitting done")) for(j in 1:1000) #Simulate 1000 1-day ahead using VineCopula { sim[j,] <- RVineSim(1, rvine) # 1000 x 112 matrix of forecasts }print(paste(i,"RVine simulation done")) for(k in 1:112) #Next: ugarchsimulation for all 112 companies { residuals2[,] <- qged(sim[,], nu = shape[k])
> > # 1000 x 112 matrix of standardized residuals residuals_temp <- residuals2[,k] # 1000 x 1 vector of standardized residuals for individual company rvine_sim <- ugarchsim(fit[[k]], n.sim=1, m.sim=1000, custom.dist = list(name=NA, distfit=residuals_temp)) #1000 simulations using the standardized residuals from Vine copula models for ugarchfit rvine_fitted[i,,k] <- fitted(rvine_sim) #Extract forecasted values - 25 x 1000 x 112 rvine_sigma[i,,k] <- sigma(rvine_sim) #Extract forecasted sigmas - 25 x 1000 x 112 for(j in 1:1000)
> > #Next: Value at risk { VaR01[,j,k] <- rvine_fitted[,j,k] + rvine_sigma[,j,k] * qdist('ged', 0.01, mu=0, sigma=1, shape = shape[k]) #Value at risk for 99% quantile VaR05[,j,k] <- rvine_fitted[,j,k] + rvine_sigma[,j,k] * qdist('ged', 0.05, mu=0, sigma=1, shape = shape[k]) #Value at risk for 95% quantile } }}remove(i, j, k) #Cleanupremove(windows, fit, residuals, shape, residuals2, residuals_temp, rvine, sim, rvine_sim) #Cleanup Hope I didn�t make any mistakes in my approach, but it seems like this is the �standard� copula + rugarch approach � if anyone is familiar with this, I am open to suggestions on how to speed up the si
> > mulations.
> > > So far, so good � the problem I am facing now:
> > > Some (only a few) of my value at risk values are positive..I have manually checked and it seems like the fitted value is much larger than the sigma, so Value at Risk is positive � which doesn�t really make any economic sense to me.
> > > Here�s a dropbox link to the returns.csv, in case anyone is interested in running my code: https://www.dropbox.com/s/69i5959f3h4kweb/returns.csv
> > >
> > > Best Regards,
> > > Ole
> > > [[alternative HTML version deleted]]
>
>
> [[alternative HTML version deleted]]
>
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