quarks

CRAN status Lifecycle: stable

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 DAX, which is implemented in the quarks package, contains daily financial data of the German stock index DAX from January 2000 to December 2021 (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.

# Calculating the returns
prices <- DAX$price.close
returns <- diff(log(prices))

Example 1 - plain historical simulation

results1 <- rollcast(x = returns, p = 0.975, method = 'plain', nout = 250,
                     nwin = 250)
#> 
#> Calculations completed.
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:    4
#> --------------------------------------------
#>  Out-of-sample losses exceeding ES
#>  
#>  Number of breaches:    1
#> --------------------------------------------

Visualize your results with the plot method implemented in quarks.

plot(results1)


Example 2 - age weighted historical simulation

results2 <- rollcast(x = returns, p = 0.975, method = 'age', nout = 250,
                     nwin = 250)
#> 
#> Calculations completed.
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:    5
#> --------------------------------------------
#>  Out-of-sample losses exceeding ES
#>  
#>  Number of breaches:    4
#> --------------------------------------------
plot(results2)


Example 3 - volatility weighted historical simulation - EWMA

results3 <- rollcast(x = returns, p = 0.975, model = 'EWMA',
                     method = 'vwhs', nout = 250, nwin = 250)
#> 
#> Calculations completed.
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:    4
#> --------------------------------------------
#>  Out-of-sample losses exceeding ES
#>  
#>  Number of breaches:    3
#> --------------------------------------------
plot(results3)


Example 4 - filtered historical simulation - GARCH

set.seed(12345)
results4 <- rollcast(x = returns, p = 0.975, model = 'GARCH',
                     method = 'fhs', nout = 250, nwin = 250, nboot = 10000)
#> 
#> Calculations completed.
results4
#>  
#> --------------------------------------------
#> |              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:    5
#> --------------------------------------------
#>  Out-of-sample losses exceeding ES
#>  
#>  Number of breaches:    2
#> --------------------------------------------
plot(results4)

To assess the performance of these methods one might apply backtesting.

For instance, by employing the Traffic Light Test, Coverage Tests or by means of Loss Function.

Example 5 - Traffic Light Test

# Calculating the returns
prices <- SP500$price.close
returns <- diff(log(prices))

results <- rollcast(x = returns, p = 0.99, model = 'GARCH',
                     method = 'vwhs', nout = 250, nwin = 500)
#> 
#> Calculations completed.
trftest(results)
#>  
#> --------------------------------------------
#> |            Backtesting result            |
#> --------------------------------------------
#>  Method: Volatility Weighting
#>  Model:  sGARCH
#> --------------------------------------------
#> |       Traffic light zone boundaries      |
#> --------------------------------------------
#>  Zone         Probability      
#>  Green zone:  p < 95%          
#>  Yellow zone: 95% <= p < 99.99%
#>  Red zone:    p >= 99.99%      
#>  
#> --------------------------------------------
#> |            Test - 99%-VaR              |
#> --------------------------------------------
#>  Number of violations: 3
#>  p = 0.7581: Green zone
#> --------------------------------------------

Example 6 - Coverage Tests

# Calculating the returns
prices <- HSI$price.close
returns <- diff(log(prices))

results <- rollcast(x = returns, p = 0.99, model = 'GARCH',
                     method = 'vwhs', nout = 250, nwin = 500)
#> 
#> Calculations completed.
cvgtest(results)
#>  
#> --------------------------------------------
#> |               Test results               |
#> --------------------------------------------
#>  
#> --------------------------------------------
#> |        Unconditional coverage test       |
#> --------------------------------------------
#> H0: w = 0.99
#> p_[uc] = 0.753
#>  
#> --------------------------------------------
#> |            Independence test             |
#> --------------------------------------------
#>  
#> H0: w_[00] = w[10]
#> p_[ind] = 0.0198
#>  
#> --------------------------------------------
#> |         Conditional coverage test        |
#> --------------------------------------------
#>  
#> H0: w_[00] = w_[10] = 0.99
#> p_[cc] = 0.0632
#> --------------------------------------------

Example 6 - Coverage Tests

# Calculating the returns
prices <- FTSE100$price.close
returns <- diff(log(prices))

results <- rollcast(x = returns, p = 0.99, model = 'GARCH',
                     method = 'vwhs', nout = 250, nwin = 500)
#> 
#> Calculations completed.
lossfun(results)
#> 
#> Please note that the following results are multiplied with 10000.
#> $lossfunc1
#> [1] 2.27884
#> 
#> $lossfunc2
#> [1] 10.84525
#> 
#> $lossfunc3
#> [1] 10.99533
#> 
#> $lossfunc4
#> [1] 10.2165

Functions

In quarks six functions are available.

Functions - version 1.0.12:

For further information on each of the functions, we refer the user to the manual or the package documentation.


Data Sets