This paper develops an approximate closed-form optimal portfolio allocation formula for a spot asset whose variance follows a GARCH(1,1) process. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected utility from terminal wealth under a...

The square-root-of-time rule (SRTR) has been used in previous Basel market risk framework to scale one day Value-at-Risk (VaR) to 10-day VaR and is extended to expected shortfall (ES) with multiple liquidity horizons in the latest Fundamental Review of the Trading Book (FRTB) Internal Model...

In this paper, we argue that certain recent findings concerning the predictive ability of tail risk exposure, defined as the extremal dependence between asset returns and market returns, are likely spurious. We argue that these results are related to biases in the estimation procedure of the...

Accurate estimation of different risk measures for financial portfolios is of utmost importance equally for financial institutions as well as regulators, however, many existing models fail to incorporate any high dimensional dependence structures adequately. To overcome this problem and capture...

Under the new regulation based on Basel solvency framework, known as Basel III and Basel IV, financial institutions must calculate the market risk capital requirements based on the Expected Shortfall (ES) measure, replacing the Value at Risk (VaR) measure. In the financial literature, there are...

Value-at-risk (VaR) is an important risk measure now widely used by financial institutions and regulators to quantify market risk and compute regulatory capital charge. The performance of VaR model can be examined by back-testing. Based on back-testing information, this paper develops a Machine...