its most compelling aspect is its vertical variation, that is, the sum of the vertical distances between its adjacent terms. Denoted by varw, the vertical variation of the sequence in (1.1) is varw = 2 + 1 + 0 + 2 + 1 = 6. Our purpose here is to compute the mean and variance of var on four classical sets of combinatorial sequences. To formalize matters and place our problem in the context of ot...

I show that the structure of the firm is not neutral in respect to regulatory capital budgeted under rules which are based on the Value-at-Risk.

The aim of this paper is to discuss the use of the Generalized Hyperbolic Distributions to fit Brazilian assets returns. Selected subclasses are compared regarding goodness of fit statistics and distances. Empirical results show that these distributions fit data well. Then we show how to use these distributions in value at risk estimation and derivative price computation.

Introduction Conclusions References

This article is devoted to the study cashflow maps used in the computation of value-at-risk (VaR). Properties and characteristics of the approaches found in the literature are presented and two new approaches are introduced. The goal of this paper is to study the quality of these maps. This is done by calculating the risk induced by the difference between the mapped cashflows and the original one.

In quantitative risk management, it is important and challenging to find sharp bounds for the distribution of the sum of dependent risks with given marginal distributions, but an unspecified dependence structure. These bounds are directly related to the problem of obtaining the worst Value-at-Risk of the total risk. Using the idea of the complete mixability, we provide a new lower bound for any...

This chapter reviews the recent developments of Value at Risk (VaR) estimation. In this survey, the most available univariate and multivariate methods are presented. The robustness and accuracy of these estimation methods are investigated based on the simulated and real data. In the backtesting procedure, the conditional coverage test (Christoffersen 1998), the dynamic quantile test (Engle and ...

Choosing a proper external risk measure is of great regulatory importance, as exemplified in the Basel II and Basel III Accords, which use value-at-risk with scenario analysis as the risk measures for setting capital requirements. We argue that a good external risk measure should be robust with respect to model misspecification and small changes in the data. A new class of data-based risk measu...