An efficient and accurate approach is proposed for forecasting Value at Risk [VaR] and Expected Shortfall [ES] measures in a Bayesian framework. This consists of a new adaptive importance sampling method for Quantile Estimation via Rapid Mixture of t approximations [QERMit]. As a first step the...

Using daily return data from the four major Central and Eastern European stock markets including fourteen highly liquid stocks and ATX (Vienna), PX (Prague), BUX (Budapest), and WIG20 (Warsaw) market indices, we model the value-at-risk using a set of univariate GARCH-type models. Our results...

The current subprime crisis has prompted us to look again into the nature of risk at the tail of the distribution. In particular, we investigate the risk contribution of an asset, which has infrequent but huge losses, to a portfolio using two risk measures, namely Value-at-Risk (VaR) and...

An inherent problem with comparing and ranking competing Value at Risk (VaR) and Expected shortfall (ES) models is that they measure only a single realization of the underlying data generation process. The question is whether there is any significant statistical difference in the performance of...

Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all of the policies at the same time. We introduce here a probabilistic approach to examine the consequences of...

The empirical joint distribution of return-pairs on stock indices displays high tail-dependence in the lower tail and low tail-dependence in the upper tail. The presence of tail-dependence is not compatible with the assumption of (conditional) joint normality. The presence of asymmetric-tail...

In this paper we 'update' the option implied probability of default (option iPoD) approach recently suggested in the literature. First, a numerically more stable objective function for the estimation of the risk neutral density is derived whose integrals can be solved analytically. Second, it is...

One of the biggest risks arising from financial operations is the risk of counterparty default, commonly known as a credit risk. Leaving unmanaged, the credit risk would, with a high probability, result in a crash of a bank. In our paper, we will focus on the credit risk quantification...

Portfolio risk is in an important way driven by 'abnormal' returns emanating from heavy tailed distributed asset returns. The theory of regular variation and extreme values provides a model for this feature of financial data. We first review this theory and subsequently study the problem of...

A class of adaptive sampling methods is introduced for efficient posterior and predictive simulation. The proposed methods are robust in the sense that they can handle target distributions that exhibit non-elliptical shapes such as multimodality and skewness. The basic method makes use of...