quarks
The goal of quarks is to enable the user to compute Value at Risk
(VaR) and Expected Shortfall (ES) by means of various types of
historical simulation. Currently plain historical simulation as well as
age-, volatility-weighted- and filtered historical simulation are
implemented in quarks. Volatility weighting can be carried out via an
exponentially weighted moving average (EWMA) model or other GARCH-type
models.
Installation
You can install the released version of quarks from CRAN with:
install.packages("quarks")Examples
The data set DAX30, which is implemented in the quarks package,
contains daily financial data of the German stock index DAX from January
2000 to December 2020 (currency in EUR). In the following examples of
the (out-of-sample) one-step forecasts of the 97.5%-VaR (red line) and
the corresponding ES (green line) are illustrated. Exceedances are
indicated by the colored circles.
library(quarks) # Call the package# Calculating the returns
prices <- DAX30$price.close
returns <- diff(log(prices))
### Example 1 - plain historical simulation
results1 <- rollcast(x = returns, p = 0.975, method = 'plain', nout = 250,
nwin = 250)
results1
#> --------------------------------------------
#> | Specifications |
#> --------------------------------------------
#> Out-of-sample size: 250
#> Rolling window size: 250
#> Bootstrap sample size: N/A
#> Confidence level: 97.5 %
#> Method: Plain
#> Model: EWMA
#> --------------------------------------------
#> | Forecast performance |
#> --------------------------------------------
#> Out-of-sample losses exceeding VaR
#>
#> Number of breaches: 16
#> --------------------------------------------
#> Out-of-sample losses exceeding ES
#>
#> Number of breaches: 7
#> --------------------------------------------
plot(results1)### Example 2 - age weighted historical simulation
results2 <- rollcast(x = returns, p = 0.975, method = 'age', nout = 250,
nwin = 250)
results2
#> --------------------------------------------
#> | Specifications |
#> --------------------------------------------
#> Out-of-sample size: 250
#> Rolling window size: 250
#> Bootstrap sample size: N/A
#> Confidence level: 97.5 %
#> Method: Age Weighting
#> Model: EWMA
#> --------------------------------------------
#> | Forecast performance |
#> --------------------------------------------
#> Out-of-sample losses exceeding VaR
#>
#> Number of breaches: 10
#> --------------------------------------------
#> Out-of-sample losses exceeding ES
#>
#> Number of breaches: 5
#> --------------------------------------------
plot(results2)### Example 3 - volatility weighted historical simulation - EWMA
results3 <- rollcast(x = returns, p = 0.975, model = 'EWMA',
method = 'vwhs', nout = 250, nwin = 250)
results3
#> --------------------------------------------
#> | Specifications |
#> --------------------------------------------
#> Out-of-sample size: 250
#> Rolling window size: 250
#> Bootstrap sample size: N/A
#> Confidence level: 97.5 %
#> Method: Volatility Weighting
#> Model: EWMA
#> --------------------------------------------
#> | Forecast performance |
#> --------------------------------------------
#> Out-of-sample losses exceeding VaR
#>
#> Number of breaches: 9
#> --------------------------------------------
#> Out-of-sample losses exceeding ES
#>
#> Number of breaches: 5
#> --------------------------------------------
plot(results3)### Example 4 - volatility weighted historical simulation - GARCH
results4 <- rollcast(x = returns, p = 0.975, model = 'GARCH',
method = 'vwhs', nout = 250, nwin = 250)
results4
#> --------------------------------------------
#> | Specifications |
#> --------------------------------------------
#> Out-of-sample size: 250
#> Rolling window size: 250
#> Bootstrap sample size: N/A
#> Confidence level: 97.5 %
#> Method: Volatility Weighting
#> Model: sGARCH
#> --------------------------------------------
#> | Forecast performance |
#> --------------------------------------------
#> Out-of-sample losses exceeding VaR
#>
#> Number of breaches: 9
#> --------------------------------------------
#> Out-of-sample losses exceeding ES
#>
#> Number of breaches: 5
#> --------------------------------------------
plot(results4)### Example 5 - filtered historical simulation - EWMA
set.seed(12345)
results5 <- rollcast(x = returns, p = 0.975, model = 'EWMA',
method = 'fhs', nout = 250, nwin = 250, nboot = 10000)
results5
#> --------------------------------------------
#> | Specifications |
#> --------------------------------------------
#> Out-of-sample size: 250
#> Rolling window size: 250
#> Bootstrap sample size: 10000
#> Confidence level: 97.5 %
#> Method: Filtered
#> Model: EWMA
#> --------------------------------------------
#> | Forecast performance |
#> --------------------------------------------
#> Out-of-sample losses exceeding VaR
#>
#> Number of breaches: 8
#> --------------------------------------------
#> Out-of-sample losses exceeding ES
#>
#> Number of breaches: 4
#> --------------------------------------------
plot(results5)### Example 6 - filtered historical simulation - GARCH
set.seed(12345)
results6 <- rollcast(x = returns, p = 0.975, model = 'GARCH',
method = 'fhs', nout = 250, nwin = 250, nboot = 10000)
results6
#> --------------------------------------------
#> | Specifications |
#> --------------------------------------------
#> Out-of-sample size: 250
#> Rolling window size: 250
#> Bootstrap sample size: 10000
#> Confidence level: 97.5 %
#> Method: Filtered
#> Model: sGARCH
#> --------------------------------------------
#> | Forecast performance |
#> --------------------------------------------
#> Out-of-sample losses exceeding VaR
#>
#> Number of breaches: 9
#> --------------------------------------------
#> Out-of-sample losses exceeding ES
#>
#> Number of breaches: 7
#> --------------------------------------------
plot(results6)To further analyze these results one might apply backtesting to assess the performance of these methods.