In this paper we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation...

We test the naive model to forecast ex-ante Value-at-Risk (VaR) using a shrinkage estimator between realized volatility estimated on past return time series, and implied volatility quoted on the market. Implied volatility is often indicated as the operators expectation about future risk, while...

In modern frameworks for financial regulation such as Basel III, IV as well as Solvency II, financial institutions are regulated to maintain a certain level of capital to prepare for potential future losses. In this paper, we take the perspective of a regulator who designs regulatory capital...

In this paper we develop a flexible and analytically tractable framework to compute the Credit Expected Shortfall in an explit if form through Kumaraswamy (1980) distribution with both default rate and recovery rate time-varying. The default rate is assumed to follow a square root process, and...