rollcast: Rolling one-step ahead forecasts of Value at Risk and...

In quarks: Simple Methods for Calculating and Backtesting Value at Risk and Expected Shortfall

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

Description

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.

Usage

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)
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)
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)
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')

### Example 4 - volatility weighted historical simulation - GARCH
results4 <- rollcast(x = returns, p = 0.975, model = 'GARCH',
                     method = 'vwhs', nout = nout, nwin = nwin)
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)
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')

### Example 6 - filtered historical simulation - GARCH
results6 <- rollcast(x = returns, p = 0.975, model = 'GARCH',
                     method = 'fhs', nout = nout, nwin = nwin, nboot = 10000)
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')

quarks documentation built on Sept. 1, 2022, 1:06 a.m.