I want to calculate the Value-at-Risk at date $t$ in such a way that I minimize the capital requirements given as \begin{align} \text{CR}_{\,t+1\,:\,t+250} = \sum_{h=0}^{249}\max\left( -(3+k_{t})\overline{\text{VaR}}^{60}_{t+h}, -\text{VaR}_{t+h}\right), \end{align} in which $\overline{\text{VaR}}^{60}_{t} = 1/60\sum_{\tau=1}^{60} \text{VaR}_{t-\tau+1}$ and $k_{t} = f(\sum_{\tau=1}^{250} H_{t-\tau+1})$ where $H_t = 1_{\left\{r_t < \text{VaR}_t\right\}}$.

The problem is that that $\text{VaR}_t$ minimizing the $\text{CR}_{t+1}$ does not necessarily minimize $\text{CR}_{\,t+1\,:\,t+250}$. Any idea how we can approach this problem is appreciated.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.