ARCH and GARCH models are widely used to model financial market volatilities in risk management applications. Considering a GARCH model with heavy-tailed innovations, we characterize the limiting distribution of an estimator of the conditional Value-at-Risk (VaR), which corresponds to the extremal quantile of the conditional distribution of the GARCH process. We propose two methods, the normal ...

In this paper we test several risk management models for computing expected shortfall for one-period hedge errors of hedged derivatives positions. Contrary to value-at-risk, expected shortfall cannot be tested using the standard binomial test, since we need information of the distribution in the tail. As derivatives positions change characteristics and thereby the size of risk exposures over ti...

This paper presents some new concepts and procedures for financial risk management. To complement the use of value at risk a new concept, upside potential or opportunity value as means to weigh opportunity loss versus risk reduction as well as an area ratio are introduced and discussed. Upper and lower bounds for risk curves corresponding to the optimal stochastic solution are developed, the ap...

Approximate Incremental Value-at-Risk formulae provide an easy-to-use preliminary guideline for risk allocation. Both the cases of risk adding and risk pooling are examined and beta-based formulae achieved. Results highlight how much the conditions for adding new risky positions are stronger than those required for risk pooling. JEL classification: C13; D81; G11; G12.

A b stra c t We propose a methodology for modelling the value at risk of a complex portfolio, based on an extension of the Ho, Stapleton and Subrahmanyam technique. We model the variance-covariance structure of up to seven variables. These could represent four country indices and three exchange rates, for example. In addition, the e®ect of an arbitrary number of orthogonal factors can be analys...

The aim of this paper is to highlight and illustrate the use of some quantitative techniques for risk estimation in finance and insurance. The first component involved in risk assessment concerns the risk measure used and the second one is based on the estimation technique. We will study the theoretical properties, the accuracy of modeling the economic phenomena and the computational performanc...

In this paper, we introduce two alternative extensions of the classical univariate Conditional-TailExpectation (CTE) in a multivariate setting. The two proposed multivariate CTEs are vector-valued measures with the same dimension as the underlying risk portfolio. As for the multivariate Value-at-Risk measures introduced by Cousin and Di Bernardino (2013), the lower-orthant CTE (resp. the upper-...

Abstract. Financial institutions have to allocate so-called economic capital in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a risk measure, i.e. a function mapping random variables to the real numbers. Nowadays value-atrisk, which is defined as a fixed level quantile of the random variable under consideratio...

In this paper we propose a downside risk measure, the expectile-based Value at Risk (EVaR), which is more sensitive to the magnitude of extreme losses than the conventional quantile-based VaR (QVaR). The index θ of an EVaR is the relative cost of the expected margin shortfall and hence reflects the level of prudentiality. It is also shown that a given expectile corresponds to the quantiles with...

The estimation of risk measured in terms of a risk measure is typically done in two steps: in the first step, the distribution is estimated by statistical methods, either parametric or nonparametric. In the second step, the estimated distribution is considered as true distribution and the targeted risk-measure is computed. In the parametric case this is achieved by using the formula for the ris...