# Manually calculating and backtesting VaR and CVaR from DCC-GARCH

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## Manually calculating and backtesting VaR and CVaR from DCC-GARCH

 I estimated a GARCH fit to the log returns of three series (CAC 40, a french real estate index and french T10 bond yield series) using `rugarch`. I then manually calculated and backtested the VaR and CVaR measures. I also fitted a DCC-GARCH(1,1) to the log returns of the 3 series using `rmgarch` and now I would like to backtest the VaR and CVaR measures in a similar way as I did for the univariate GARCH cases. We'll need to specify the following functions for the CVaR before we proceed:     #This function calculates the CVaR at a certain position gdist list     cvar <- function(p=0.05, s = "CAC", dist_params = gdist_var, pos = l, v = df, dist = "jsu"){       ES <- abs((integrate(qdist, lower = 0, upper = p, distribution = dist, mu = gdist_var[[s]][, 'Mu'][pos], sigma = gdist_var[[s]][, 'Sigma'][pos],                            shape = gdist_var[[s]][, 'Shape'][pos], skew = gdist_var[[s]][, 'Skew'][pos])\$value)/p * v[nrow(v),s])       return(ES)     }     #This function calculates the CVaR given the arguments     cvar_df <- function(p=0.01, dist = "jsu", mu = Mu, sigma = Sigma, shape = Shape, skew = Skew){       ES <- (integrate(qdist, lower = 0, upper = p, distribution = dist, mu = mu, sigma = sigma, shape = shape, skew = skew)\$value)/p       return(ES)     }     #This function is a vectorized form of the above     vcvar_df <- Vectorize(cvar_df) The data can be found on dropbox under the following links (one for french real estate index data and the other for french bonds) the CAC 40 data is downloadable with `quantmod`: https://www.dropbox.com/s/vy8sl88fs5opmi3/IEIF%20SIIC%20FRANCE_quote_chart.csv?dl=0https://www.dropbox.com/s/xljxk5izy6pt1ds/entre_obligations.csv?dl=0The commented code is the following:     #loading libraries and data:     require(tidyquant)     require(reshape2)     require(astsa)     require(GGally)     require(forecast)     source("functions.R", local = T)     # # https://www.banque-france.fr/statistiques/taux-et-cours/les-indices-obligataires    obli_10 <- read.csv("entre_obligations.csv", sep = ";", na.strings = "-", stringsAsFactors = F) %>%       rename(Date = 1) %>%       mutate(Date = dmy(Date)) %>%       mutate_at(vars(-Date), funs(gsub("\\,", ".", .))) %>%       mutate_at(vars(-Date), funs(as.numeric)) %>%       dplyr::select(c(1,2))     # #https://live.euronext.com/en/product/indices/QS0010980447-XPAR/quotesindices nu de:     # # https://www.ieif.fr/wp-content/plugins/aa-indices/datas/histo/index.php?IndiceNu=SIICNu&IndiceNet=SIICNet&IndiceBrut=SIICBrut&Indice=Euronext%20IEIF%20SIIC%20France    reit <- read.csv("IEIF SIIC FRANCE_quote_chart.csv", stringsAsFactors = F) %>%       dplyr::select(1,2) %>%       rename(Date = 1) %>%       mutate(Date = substr(Date, 1, 10)) %>%       mutate(Date = ymd(Date))     cac <- as.data.frame(Ad(getSymbols("^FCHI", src = "yahoo", adjust = T, auto.assign = FALSE)))     cac <- cac %>%       mutate(Date = rownames(.)) %>%       mutate(Date = ymd(Date)) %>%       dplyr::select(Date, everything())     #Calculate the log returns     lr_df <- as.data.frame(sapply(df[2:ncol(df)], function(x) diff(log(x))))     lr_df <-cbind(df\$Date[2:nrow(df)], lr_df) %>%       dplyr::rename(Date = !!names(.)[1])     #Specification of GARCH models     cac_egarch_spec <- ugarchspec(mean.model = list(armaOrder = c(3, 3), include.mean = T, archm = F, archpow = 1),                                   variance.model = list(model = "eGARCH", garchOrder = c(2, 1)),                                   distribution.model="jsu")     reit_egarch_spec <- ugarchspec(mean.model = list(armaOrder = c(3, 1), include.mean = T, archm = F, archpow = 1),                                    variance.model = list(model = "eGARCH", garchOrder = c(2, 1)),                                    distribution.model="nig")     obli_apgarch_spec <- ugarchspec(mean.model = list(armaOrder = c(2, 1), include.mean = T, archm = F, archpow = 1),                                      variance.model = list(model = "apARCH", garchOrder = c(1, 1)),                                      distribution.model="jsu")     #Get VaR and CVaR     cac_roll <- ugarchroll(cac_egarch_spec, lr_df[,2],n.start = 750, refit.every = 50, refit.window = "moving",                                        solver = "hybrid", calculate.VaR = TRUE, VaR.alpha = c(0.01, 0.025, 0.05), keep.coef = T,                                        fit.control = list(scale = 1))     reit_roll <- ugarchroll(reit_egarch_spec, lr_df[,3],n.start = 750, refit.every = 50, refit.window = "moving",                            solver = "hybrid", calculate.VaR = TRUE, VaR.alpha = c(0.01, 0.025, 0.05), keep.coef = T,                            fit.control = list(scale = 1))     obli_roll <- ugarchroll(obli_apgarch_spec, lr_df[,4],n.start = 750, refit.every = 50, refit.window = "moving",                             solver = "hybrid", calculate.VaR = TRUE, VaR.alpha = c(0.01, 0.025, 0.05), keep.coef = T,                             fit.control = list(scale = 1))     gdist_var <- list()     gdist_var[["CAC"]] <- as.data.frame(cac_roll, which = 'density')     gdist_var[["REIT"]] <- as.data.frame(reit_roll, which = 'density')     gdist_var[["OBLI_10"]] <- as.data.frame(obli_roll, which = 'density')     #VaR and CVaR calculations     p <- c(0.05, 0.025, 0.01)     l <- nrow(gdist_var[["CAC"]])     for(j in p){       for(i in 1:3){         print(paste("VaR", names(gdist_var)[i], 1-j))         print(abs(qdist(dg[[i]], p=j, mu=gdist_var[[i]]\$Mu[l], sigma=gdist_var[[i]]\$Sigma[l], skew=gdist_var[[i]]\$Skew[l], shape=gdist_var[[i]]\$Shape[l]))*df[nrow(df),i+1])       }     }     for(j in p){       for(i in 1:3){         print(paste("CVaR", names(gdist_var)[i], 1-j))         print(cvar(p = j, s = names(gdist_var)[i], dist_params = gdist_var, pos = l, v = df, dist = dg[[i]]))       }     }     #VaR plots for cac only but will be done for others the same way     var_cac <- gdist_var\$CAC     var_cac <- cbind.data.frame(tail(lr_df[,c("Date","CAC")],2438), var_cac) %>%       dplyr::select(-`Shape(GIG)`, -Realized) %>%       dplyr::mutate(VaR_99 = qdist("jsu", p = 0.01, mu = Mu, sigma = Sigma, skew = Skew, shape = Shape)) %>%       dplyr::select(-Mu, -Sigma, -Skew, -Shape)     var_cac <- melt(var_cac, id.vars = "Date")     ggplot(data = var_cac, aes(x = Date, value)) + geom_line(aes(colour = variable)) +       ggtitle("Series with 1% 1D VaR Limit") +       theme(plot.title = element_text(hjust = 0.5))     #VaR backtesting reports using report function     report(cac_roll, type = "VaR", VaR.alpha = 0.05, conf.level = 0.95)     report(reit_roll, type = "VaR", VaR.alpha = 0.05, conf.level = 0.95)     report(obli_roll, type = "VaR", VaR.alpha = 0.05, conf.level = 0.95)     #CVaR plots for CAC only but will be done for others     cvar_cac <- gdist_var\$CAC     cvar_cac <- cbind.data.frame(tail(lr_df[,c("Date","CAC")],2438), cvar_cac) %>%       dplyr::select(-`Shape(GIG)`, -Realized) %>%       dplyr::mutate(CVaR_99 = vcvar_df(p = 0.01, dist = "jsu", mu = Mu, sigma = Sigma, shape = Shape, skew = Skew)) %>%       dplyr::select(-Mu, -Sigma, -Skew, -Shape)     mcvar_cac <- melt(cvar_cac, id.vars = "Date")     ggplot(data = mcvar_cac, aes(x = Date, value)) + geom_line(aes(colour = variable)) +       ggtitle("Series with 1% 1D CVaR Limit") +       theme(plot.title = element_text(hjust = 0.5))     #Bactesting CVaRby calculating nuber of times CVaR crossed     cvar_cac <- gdist_var\$CAC     cvar_cac <- cbind.data.frame(tail(lr_df[,c("Date","CAC")],2438), cvar_cac) %>%       dplyr::select(-`Shape(GIG)`, -Realized) %>%       dplyr::mutate(CVaR_99 = vcvar_df(p = 0.01, dist = "jsu", mu = Mu, sigma = Sigma, shape = Shape, skew = Skew)) %>%       dplyr::mutate(CVaR_975 = vcvar_df(p = 0.025, dist = "jsu", mu = Mu, sigma = Sigma, shape = Shape, skew = Skew)) %>%       dplyr::mutate(CVaR_95 = vcvar_df(p = 0.05, dist = "jsu", mu = Mu, sigma = Sigma, shape = Shape, skew = Skew)) %>%       mutate(depasse_99 = case_when(CVaR_99 >= .[[2]] ~ 1, TRUE ~ 0)) %>%       mutate(depasse_975 = case_when(CVaR_975 >= .[[2]] ~ 1, TRUE ~ 0)) %>%       mutate(depasse_95 = case_when(CVaR_95 >= .[[2]] ~ 1, TRUE ~ 0)) %>%       mutate(sum_99 = sum(depasse_99)) %>%       mutate(sum_975 = sum(depasse_975)) %>%       mutate(sum_95 = sum(depasse_95))     #DCC GARCH of GARCH models above:     require(rmgarch)     dcc_garch <- multispec(c(cac_egarch_spec, reit_egarch_spec, obli_apgarch_spec))     dcc_multfit <- multifit(dcc_garch, lr_df[,2:ncol(lr_df)]) #fitting many univariate models     dcc_spec <- dccspec(uspec = dcc_garch, dccOrder = c(1,1), distribution = "mvnorm")     dcc_fit <- dccfit(dcc_spec, lr_df[,2:ncol(lr_df)], fit.control = list(eval.se = TRUE), fit = dcc_multfit) #fit = dcc_multfit not really necessary but more robust     dcc_roll <- dccroll(dcc_spec, lr_df[,2:4],n.start = 750, refit.every = 50, refit.window = "moving",                            solver = "solnp", calculate.VaR = TRUE, VaR.alpha = c(0.01, 0.025, 0.05), keep.coef = T,                            fit.control = list(scale = 1)) Now I want to do the backtesting and plotting steps for both 1Day VaR and 1Day CVaR measures. Ideally I would also conduct the Kupiec and Christoffersen test just like in the function `report` of the package `rugarch`. I am realy stumped as I tried to find an answer online but couldn't. -- Eliot TABET | Structurer/Quantitative Analyst Les informations contenues dans ce message sont confidentielles. Si vous receviez ce message par erreur, merci de prévenir l'expéditeur et de le supprimer ainsi que ses pièces jointes. N'imprimez ce mail que si c'est nécessaire         [[alternative HTML version deleted]] _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.