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Value at Risk and Expected Shortfall for several days ahead

Source: R/risk.R
forecast_var_es.Rd

Simulates future returns with predict.stochvolTMB and calculates the Value at Risk (VaR) and Expected Shortfall (ES) for each day ahead, both of the return on that day and of the cumulative return (the sum of the log-returns) up to that day. The cumulative values for step = 10 are, for example, the 10-day VaR and ES.

Usage

forecast_var_es(
  object,
  steps = 10L,
  level = c(0.95, 0.99),
  nsim = 100000L,
  include_parameters = TRUE
)

Arguments

object

A stochvolTMB object returned from estimate_parameters.

steps

Number of days ahead.

level

Vector of confidence levels between 0.5 and 1.

nsim

Number of simulated paths.

include_parameters

Logical. If TRUE, the parameters are drawn from their asymptotic distribution for each path. See predict.stochvolTMB.

Value

A data.table with the columns step, level, var, es, var_cumulative and es_cumulative.

Details

VaR and ES are reported as positive numbers when they are losses: if \(q\) is the \(1 - \alpha\) quantile of the simulated returns, then \(VaR = -q\) and \(ES = -E[y \mid y \le q]\). By default, the simulation includes the uncertainty of the parameters. The Monte Carlo error decreases with nsim. For one day ahead, var_es is exact and faster.

See also

var_es

Examples

# \donttest{
opt <- estimate_parameters(spy$log_return, model = "skew_t_leverage", silent = TRUE)
set.seed(1)
forecast_var_es(opt, steps = 10, level = 0.99)
#>      step level        var         es var_cumulative es_cumulative
#>     <int> <num>      <num>      <num>          <num>         <num>
#>  1:     1  0.99 0.05321239 0.06872867     0.05321239    0.06872867
#>  2:     2  0.99 0.05466494 0.07102813     0.07654920    0.09854347
#>  3:     3  0.99 0.05392145 0.07070557     0.09661490    0.12275207
#>  4:     4  0.99 0.05404943 0.07126835     0.11197686    0.14337785
#>  5:     5  0.99 0.05398812 0.07171376     0.12566563    0.16325650
#>  6:     6  0.99 0.05388871 0.07200359     0.13942413    0.17975980
#>  7:     7  0.99 0.05431752 0.07300936     0.15104218    0.19599194
#>  8:     8  0.99 0.05406979 0.07313807     0.16243718    0.21102743
#>  9:     9  0.99 0.05427650 0.07360896     0.17503939    0.22806235
#> 10:    10  0.99 0.05287490 0.07258450     0.18626579    0.24215530
# }