Normal: \(VaR = -(\mu + \sigma z_\alpha)\) and
\(ES = -\mu + \sigma \phi(z_\alpha)/\alpha\), both reported as
positive losses. Mirrors morie.fn.volgvi and
morie.fn.volges.
Usage
morie_garch_var_es(mu, sigma, alpha = 0.05, dist = "normal", nu = 8)
Arguments
- mu
conditional mean forecast.
- sigma
one-step volatility (standard deviation).
- alpha
tail probability in (0, 1).
- dist
"normal" or "t".
- nu
degrees of freedom for the t (> 2).
Value
list: var, es, quantile, alpha, dist.
References
Artzner, P., Delbaen, F., Eber, J.-M. & Heath, D.
(1999). Coherent measures of risk. Mathematical Finance, 9(3),
203-228.
Examples
morie_garch_var_es(0, 1, 0.05)$var
#> [1] 1.644854
