Under the revised market risk framework of the Basel Committee on Banking Supervision, the model validation regime for internal models now requires that models capture the tail risk in profit-and-loss (P&L) distributions at the trading desk level. We develop multi-desk backtests, which...

Portfolio credit risk is often concerned with the tail distribution of the total loss, defined to be the sum of default losses incurred from a collection of individual loans made out to the obligors. The default for an individual loan occurs when the assets of a company (or individual) fall...

One of the key components of financial risk management is risk measurement. This typically requires modeling, estimating and forecasting tail-related quantities of the asset returns’ conditional distribution. Recent advances in the financial econometrics literature have developed several...

Evaluating risk measures, premiums, and capital allocation based on dependent multi-losses is a notoriously difficult task. In this paper, we demonstrate how this can be successfully accomplished when losses follow the multivariate Pareto distribution of the second kind, which is an attractive...

This paper proposes a new method to introduce coherent risk measures for risks with infinite expectation, such as those characterized by some Pareto distributions. Extensions of the conditional value at risk, the weighted conditional value at risk and other examples are given. Actuarial...

This article is concerned with the study of the tail correlation among equity indices by means of dynamic copula functions. The main idea is to consider the impact of the use of copula functions in the accuracy of the model´s parameters and in the computation of Value-at-Risk (VaR). Results...

The precise large deviations asymptotics for the sums of independent identical random variables when the distribution of the summand belongs to the class S * S* of heavy tailed distributions is studied. Under mild conditions, we extend the previous results from the paper Denisov et al. (2010) to...

According to the last proposals of the Basel Committee on Banking Supervision, banks or insurance companies under the advanced measurement approach (AMA) must use four different sources of information to assess their operational risk capital requirement. The fourth includes ’business...

One way to formulate a multivariate probability distribution with dependent univariate margins distributed gamma is by using the closure under convolutions property. This direction yields an additive background risk model, and it has been very well-studied. An alternative way to accomplish the...

The appropriate choice of a threshold level, which separates the tails of the probability distribution of a random variable from its middle part, is considered to be a very complex and challenging task. This paper provides an empirical study on various methods of the optimal tail selection in...