Rolling one-step ahead forecasts of Value at Risk and Expected Shortfall

Computes rolling one-step ahead forecasts of Value at Risk and Expected Shortfall (Conditional Value at Risk) by means of plain historical simulation age- and volatility-weighted historical simulation as well as filtered historical simulation.

rollcast(
  x,
  p = 0.975,
  model = c("EWMA", "GARCH"),
  method = c("plain", "age", "vwhs", "fhs"),
  lambda = c(0.94, 0.98),
  nout = NULL,
  nwin = NULL,
  nboot = NULL,
  smoothscale = c("none", "lpr", "auto"),
  smoothopts = list(),
  ...
)

Arguments

x

a numeric vector of asset returns

p

confidence level for VaR calculation; default is 0.975

model

model for estimating conditional volatility; options are 'EWMA' and 'GARCH'; if model = 'GARCH', additional arguments can be adjusted via ...; default is 'EWMA'

method

method to be used for calculation; default is 'plain'

lambda

decay factor for the calculation of weights; default is 0.98 for method = 'age' and 0.94 for method = 'vwhs' or method = 'fhs'

nout

number of out-of-sample observations; most recent observations are used; default is NULL

nwin

window size for rolling one-step forecasting; most recent observations before out-of-sample are used; default is NULL

nboot

size of bootstrap sample; must be a single non-NA integer value with nboot > 0; default is NULL

smoothscale

a character object; defines the smoothing approach for the unconditional variance from the logarithm of the squared centralized returns; for smoothscale = 'lpr', the unconditional variance is smoothed via the smoots::gsmooth() function from the smoots package; the bandwidth has to be chosen manually; otherwise the default is used; if smoothscale = 'auto', the function smoots::msmooth() is employed and the bandwidth is chosen automatically (data-driven); see the documentation of the smoots package for more information; is set to smoothscale = 'none' by default

smoothopts

additional arguments of smoots::gsmooth() and smoots::msmooth(); see the documentation of the smoots package for more information; is set to customized default settings

...

additional arguments of the ugarchspec function from the rugarch-package; only applied if model = 'GARCH'; default settings for the arguments variance.model and mean.model are:

variance.model = list(model = 'sGARCH', garchOrder = c(1, 1))
mean.model = list(armaOrder = c(0, 0))

Value

Returns a list with the following elements:

VaR: Numerical vector containing out-of-sample forecasts of Value at Risk
ES: Numerical vector containing out-of-sample forecasts of Expected Shortfall (Conditional Value at Risk)
xout: Numerical vector containing out-of-sample returns
p: Confidence level for VaR calculation
model: Model for estimating conditional volatility
method: Method to be used for calculation
nout: Number of out-of-sample observations
nwin: Window size for rolling one-step forecasting
nboot: Size of bootstrap sample

Examples


prices <- DAX$price.close
returns <- diff(log(prices))
n <- length(returns)
nout <- 250 # number of obs. for out-of-sample forecasting
nwin <- 500 # window size for rolling forecasts


### Example 1 - plain historical simulation
results1 <- rollcast(x = returns, p = 0.975, method = 'plain', nout = nout,
                     nwin = nwin)
#> 
#> Calculations completed.
matplot(1:nout, cbind(-results1$xout, results1$VaR, results1$ES),
  type = 'hll',
  xlab = 'number of out-of-sample obs.', ylab = 'losses, VaR and ES',
  main = 'Plain HS - 97.5% VaR and ES for the DAX30 return series')


### Example 2 - age weighted historical simulation
results2 <- rollcast(x = returns, p = 0.975, method = 'age', nout = nout,
                     nwin = nwin)
#> 
#> Calculations completed.
matplot(1:nout, cbind(-results2$xout, results2$VaR, results2$ES),
  type = 'hll',
  xlab = 'number of out-of-sample obs.', ylab = 'losses, VaR and ES',
  main = 'Age weighted HS - 97.5% VaR and ES for the DAX30 return series')


### Example 3 - volatility weighted historical simulation - EWMA
results3 <- rollcast(x = returns, p = 0.975, model = 'EWMA',
                     method = 'vwhs', nout = nout, nwin = nwin)
#> 
#> Calculations completed.
matplot(1:nout, cbind(-results3$xout, results3$VaR, results3$ES),
  type = 'hll',
  xlab = 'number of out-of-sample obs.', ylab = 'losses, VaR and ES',
  main = 'Vol. weighted HS (EWMA) - 97.5% VaR and ES for the DAX30 return
  series')

# \donttest{
### Example 4 - volatility weighted historical simulation - GARCH
results4 <- rollcast(x = returns, p = 0.975, model = 'GARCH',
                     method = 'vwhs', nout = nout, nwin = nwin)
#> 
#> Calculations completed.
matplot(1:nout, cbind(-results4$xout, results4$VaR, results4$ES),
  type = 'hll',
  xlab = 'number of out-of-sample obs.', ylab = 'losses, VaR and ES',
  main = 'Vol. weighted HS (GARCH) - 97.5% VaR and ES for the DAX30 return
  series')

# }
### Example 5 - filtered historical simulation - EWMA
results5 <- rollcast(x = returns, p = 0.975, model = 'EWMA',
                     method = 'fhs', nout = nout, nwin = nwin, nboot = 10000)
#> 
#> Calculations completed.
matplot(1:nout, cbind(-results5$xout, results5$VaR, results5$ES),
  type = 'hll',
  xlab = 'number of out-of-sample obs.', ylab = 'losses, VaR and ES',
  main = 'Filtered HS (EWMA) - 97.5% VaR and ES for the DAX30 return
  series')

# \donttest{
### Example 6 - filtered historical simulation - GARCH
results6 <- rollcast(x = returns, p = 0.975, model = 'GARCH',
                     method = 'fhs', nout = nout, nwin = nwin, nboot = 10000)
#> 
#> Calculations completed.
matplot(1:nout, cbind(-results6$xout, results6$VaR, results6$ES),
  type = 'hll',
  xlab = 'number of out-of-sample obs.', ylab = 'losses, VaR and ES',
  main = 'Filtered HS (GARCH) - 97.5% VaR and ES for the DAX30 return
  series')

# }