- Joint value at risk: a new conditional risk measure
- Mensali, Elisabetta <1994>
Subject
- SECS-S/01 Statistica
Description
- In this PhD thesis a new firm level conditional risk measure is developed. It is named Joint Value at Risk (JVaR) and is defined as a quantile of a conditional distribution of interest, where the conditioning event is a latent upper tail event. It addresses the problem of how risk changes under extreme volatility scenarios. The properties of JVaR are studied based on a stochastic volatility representation of the underlying process. We prove that JVaR is leverage consistent, i.e. it is an increasing function of the dependence parameter in the stochastic representation. A feasible class of nonparametric M-estimators is introduced by exploiting the elicitability of quantiles and the stochastic ordering theory. Consistency and asymptotic normality of the two stage M-estimator are derived, and a simulation study is reported to illustrate its finite-sample properties. Parametric estimation methods are also discussed. The relation with the VaR is exploited to introduce a volatility contribution measure, and a tail risk measure is also proposed. The analysis of the dynamic JVaR is presented based on asymmetric stochastic volatility models. Empirical results with S&P500 data show that accounting for extreme volatility levels is relevant to better characterize the evolution of risk. The work is complemented by a review of the literature, where we provide an overview on quantile risk measures, elicitable functionals and several stochastic orderings.
Date
- 2023-06-15
- info:eu-repo/date/embargoEnd/2025-06-16
Type
- Doctoral Thesis
- PeerReviewed
Format
- application/pdf
Identifier
urn:nbn:it:unibo-29461
Mensali, Elisabetta (2023) Joint value at risk: a new conditional risk measure, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Scienze statistiche