The two-sided Weibull distribution and forecasting financial tail risk

Abstract

A two-sided Weibull is developed to model the conditional financial return distribution, for the purpose of forecasting Value at Risk (VaR) and conditional VaR. A range of conditional return distributions are combined with four volatility specifications to forecast tail risk in four international markets, two exchange rates and one individual asset series, over a four year forecast period that includes the recent global financial crisis. The two-sided Weibull performs at least as well as other distributions for VaR forecasting, but performs most favourably for conditional Value at Risk forecasting, prior to as well as during and after the recent crisis. A range of conditional return distributions are combined with four volatility specifications to forecast tail risk in four international markets, two exchange rates and one individual asset series, over a four year forecast period that includes the recent global financial crisis. The two-sided Weibull performs at least as well as other distributions for VaR forecasting, but performs most favourably for conditional Value at Risk forecasting, prior to as well as during and after the recent crisis.

Value-at-Risk for fixed-income portfolios: a Kalman filtering approach

“…The unconditional coverage test is the standard tool for backtesting models and is also recommended (see, e.g. Chen and Gerlach (2011)) by Basel II. Hence we decided to employ it throughout the numerical experiments in this paper, in addition to the conditional coverage tests which are described later in this section.…”

“…Quantitative risk measures have become crucial management instruments for portfolio managers for this purpose. Value-at-Risk (VaR) has been chosen by the Basel Committee on Banking Supervision in Basel II as the standard risk measure for financial risk managers, see Basel Committee (2006) and Chen and Gerlach (2011) for details. VaR has received criticism by Artzner et al (1999), Acerbi and Tasche (2002) and Szegö (2002) for not being a coherent measure of risk.…”

Semiparametric Two-Component Mixture Models When One Component Is Defined Through Linear Constraints

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On the convergence of distributions of statistics constructed from samples of random size to a multivariate generalized variance-gamma distributions

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“…Let θ n be ‫ޒ‬ m valued vectors, n ∈ ‫.ގ‬ In this section, we assume that the random vectors S n, k have the form S n, k = T n, k -θ n , n, k ∈ ‫.ގ‬ As concerns the normaliz ing constants and vectors, we assume that there exist m vectors a, a n , b, and b n and positive numbers σ n such that (4) and, for all n, k ∈ ‫,ގ‬ (5) so that…”