TL-methods function

Method to backtest VaR violation using the Traffic Light (TL) approach of Basel

A method that performs backtest for VaR models using the TL approach. According to Basel, a VaR model is deemed valid if the cumulative probability of observing up to $n_f$ failures is less than 0.95 (green zone) under the binomial distribution with $n$ (sample size) and Var level as the parameters. If the cumulative probability is between 0.95 and 0.9999 a VaR model is in yellow zone. Otherwise (>0.9999) a VaR model is in red zone. methods

TL(y, n = NULL, no_fail = NULL, VaR, VaR_level)

## S4 method for signature 'ANY'
TL(y, n = NULL, no_fail = NULL, VaR, VaR_level)

Arguments

• y: The time series to apply a VaR model (a single asset rerurn or portfolio return).
• n: If y is not provided, then insert sample size. Default is NULL.
• no_fail: If y is not provided, then insert number of fails. Default is NULL.
• VaR: The forecast VaR.
• VaR_level: The VaR level, typically 95% or 99%.

Examples

pw.CCC.obj = new("simMGarch")
pw.CCC.obj@d = 10
pw.CCC.obj@n = 1000
pw.CCC.obj@changepoints = c(250,750)
pw.CCC.obj = pc_cccsim(pw.CCC.obj)
y_out_of_sample = t(pw.CCC.obj@y[,900:1000])
w=rep(1/pw.CCC.obj@d,pw.CCC.obj@d) #an equally weighted portfolio
#VaR = quantile(t(pw.CCC.obj@y[,1:899])%*%w,0.05)
#ts.plot(y_out_of_sample%*%w,ylab="portfolio return");abline(h=VaR,col="red")
#TL(y=y_out_of_sample%*%w,VaR=rep(VaR,100),VaR_level = 0.95)

References

Basle Committee on Banking Supervision (1996). "Supervisory Framework for the Use of ‘Backtesting’ in Conjunction with the Internal Models Approach to Market Risk Capital Requirements".