A flexible framework for the analysis of tail events is proposed. The framework contains tail moment measures that allow for Expected Shortfall (ES) estimation. Connecting the implied tail thickness of a family of distributions with the quantile and expectile estimation, a platform for risk...

In this paper we provide a review of copula theory with applications to finance. We illustrate the idea on the bivariate framework and discuss the simple, elliptical and Archimedean classes of copulae. Since the copulae model the dependency structure between random variables, next we explain the...

In this paper we propose a new measure for systemic risk: the Financial Risk Meter (FRM). This measure is based on the penalization parameter () of a linear quantile lasso regression. The FRM is calculated by taking the average of the penalization parameters over the 100 largest US publicly...

We argue that the practise of valuing the portfolio is important for the calculation of the VaR. In particular, the seller (buyer) of an asset does not face horizontal demand (supply) curves. We propose a partially new approach for incorporating this fact in the VaR and in an empirical...

Tail risk refers to the possibility that a rare event would adversely affect the value of a portfolio in a significant manner. It became much more relevant due to recent periods of strong market turbulence.We describe how to quantify such risk, which tail risk protection strategies were...

[Update: Within four weeks of the original publication of this research report, Risk Magazine reported in its 28th February 2012 issue story titled 'Goodbye VaR? Basel to Consider Other Risk Metrics': "A review of trading book capital rules, due to be launched in March by the Basel Committee on...

In aftermath of the Financial Crisis, some risk management practitioners advocate wider adoption of Bayesian inference to replace Value-at-Risk (VaR) models for minimizing risk failures (Borison & Hamm, 2010). They claim reliance of Bayesian inference on subjective judgment, the key limitation...

The September 2008 collapse of Lehman Brothers was the 9/11 on Wall Street, and many articles had been written on the changes in the global risk landscape that followed. However, there is scarcity of rigorous studies using empirical data and advanced econometric methods to verify such a change...

In the aftermath of the Global Financial Crisis, some risk management practitioners have advocated wider adoption of Bayesian inference to replace Value- at-Risk (VaR) models in order to minimize risk failures. Despite its limitations, the Bayesian methodology has significant advantages. Just...