Filtered historical simulation

Calculates univariate Value at Risk and Expected Shortfall (Conditional Value at Risk) by means of filtered historical simulation. Volatility can be estimated with an exponentially weighted moving average or a GARCH-type model.

fhs(x, p = 0.975, model = c("EWMA", "GARCH"), lambda = 0.94, nboot = NULL, ...)

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'

lambda

decay factor for the calculation of weights; default is 0.94

nboot

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

...

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

Calculated Value at Risk

ES

Calculated Expected Shortfall (Conditional Value at Risk)

p

Confidence level for VaR calculation

garchmod

The model fit. Is the respective GARCH fit for model = "GARCH" (see rugarch documentation) and 'EWMA' for model = "EWMA"

Examples

prices <- DAX$price.close
returns <- diff(log(prices))
# volatility weighting via EWMA
ewma <- fhs(x = returns, p = 0.975, model = "EWMA", lambda = 0.94,
            nboot = 10000)
ewma
#> $VaR
#> [1] 0.02399405
#> 
#> $ES
#> [1] 0.03057634
#> 
#> $p
#> [1] 0.975
#> 
#> $garchmod
#> [1] "EWMA"
#> 
# volatility weighting via GARCH
garch <- fhs(x = returns, p = 0.975, model = "GARCH", variance.model =
list(model = "sGARCH"), nboot = 10000)
garch
#> $VaR
#> [1] 0.02300646
#> 
#> $ES
#> [1] 0.02917895
#> 
#> $p
#> [1] 0.975
#> 
#> $garchmod
#> 
#> *---------------------------------*
#> *          GARCH Model Fit        *
#> *---------------------------------*
#> 
#> Conditional Variance Dynamics 	
#> -----------------------------------
#> GARCH Model	: sGARCH(1,1)
#> Mean Model	: ARFIMA(0,0,0)
#> Distribution	: norm 
#> 
#> Optimal Parameters
#> ------------------------------------
#>         Estimate  Std. Error  t value Pr(>|t|)
#> mu      0.000662    0.000141   4.6989 0.000003
#> omega   0.000003    0.000001   2.9225 0.003473
#> alpha1  0.094987    0.009186  10.3409 0.000000
#> beta1   0.890729    0.010221  87.1483 0.000000
#> 
#> Robust Standard Errors:
#>         Estimate  Std. Error  t value Pr(>|t|)
#> mu      0.000662    0.000129  5.13189 0.000000
#> omega   0.000003    0.000004  0.65098 0.515059
#> alpha1  0.094987    0.027338  3.47457 0.000512
#> beta1   0.890729    0.035855 24.84286 0.000000
#> 
#> LogLikelihood : 16665.98 
#> 
#> Information Criteria
#> ------------------------------------
#>                     
#> Akaike       -5.9710
#> Bayes        -5.9662
#> Shibata      -5.9710
#> Hannan-Quinn -5.9693
#> 
#> Weighted Ljung-Box Test on Standardized Residuals
#> ------------------------------------
#>                         statistic p-value
#> Lag[1]                     0.2708  0.6028
#> Lag[2*(p+q)+(p+q)-1][2]    0.5562  0.6678
#> Lag[4*(p+q)+(p+q)-1][5]    1.5043  0.7388
#> d.o.f=0
#> H0 : No serial correlation
#> 
#> Weighted Ljung-Box Test on Standardized Squared Residuals
#> ------------------------------------
#>                         statistic   p-value
#> Lag[1]                      5.111 0.0237737
#> Lag[2*(p+q)+(p+q)-1][5]    13.799 0.0009311
#> Lag[4*(p+q)+(p+q)-1][9]    16.489 0.0015467
#> d.o.f=2
#> 
#> Weighted ARCH LM Tests
#> ------------------------------------
#>             Statistic Shape Scale   P-Value
#> ARCH Lag[3]     13.33 0.500 2.000 0.0002605
#> ARCH Lag[5]     13.75 1.440 1.667 0.0007851
#> ARCH Lag[7]     13.81 2.315 1.543 0.0022585
#> 
#> Nyblom stability test
#> ------------------------------------
#> Joint Statistic:  19.193
#> Individual Statistics:             
#> mu     0.0759
#> omega  3.0459
#> alpha1 0.2056
#> beta1  0.1792
#> 
#> Asymptotic Critical Values (10% 5% 1%)
#> Joint Statistic:     	 1.07 1.24 1.6
#> Individual Statistic:	 0.35 0.47 0.75
#> 
#> Sign Bias Test
#> ------------------------------------
#>                    t-value      prob sig
#> Sign Bias           2.0500 4.041e-02  **
#> Negative Sign Bias  0.3604 7.185e-01    
#> Positive Sign Bias  3.6506 2.640e-04 ***
#> Joint Effect       43.7545 1.702e-09 ***
#> 
#> 
#> Adjusted Pearson Goodness-of-Fit Test:
#> ------------------------------------
#>   group statistic p-value(g-1)
#> 1    20     179.4    4.065e-28
#> 2    30     193.7    2.815e-26
#> 3    40     224.3    6.938e-28
#> 4    50     244.4    9.269e-28
#> 
#> 
#> Elapsed time : 0.8042977 
#> 
#>