Browsing by Subject "Value-at-risk"

Now showing 1 - 3 of 3

Open Access
High volatility, thick tails and extreme value theory in value-at-risk estimation
(Elsevier BV, 2003) Gençay, R.; Selçuk, F.; Ulugülyaǧci, A.
In this paper, the performance of the extreme value theory in value-at-risk calculations is compared to the performances of other well-known modeling techniques, such as GARCH, variance-covariance (Var-Cov) method and historical simulation in a volatile stock market. The models studied can be classified into two groups. The first group consists of GARCH(1, 1) and GARCH(1, 1)- t models which yield highly volatile quantile forecasts. The other group, consisting of historical simulation, Var-Cov approach, adaptive generalized Pareto distribution (GPD) and nonadaptive GPD models, leads to more stable quantile forecasts. The quantile forecasts of GARCH(1, 1) models are excessively volatile relative to the GPD quantile forecasts. This makes the GPD model be a robust quantile forecasting tool which is practical to implement and regulate for VaR measurements. © 2003 Elsevier B.V. All rights reserved.
Open Access
Robust portfolio choice with CVaR and VaR under distribution and mean return ambiguity
(Springer, 2014-01-09) Paç, A. B.; Pınar, M. Ç.
We consider the problem of optimal portfolio choice using the Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR) measures for a market consisting of n risky assets and a riskless asset and where short positions are allowed. When the distribution of returns of risky assets is unknown but the mean return vector and variance/covariance matrix of the risky assets are fixed, we derive the distributionally robust portfolio rules. Then, we address uncertainty (ambiguity) in the mean return vector in addition to distribution ambiguity, and derive the optimal portfolio rules when the uncertainty in the return vector is modeled via an ellipsoidal uncertainty set. In the presence of a riskless asset, the robust CVaR and VaR measures, coupled with a minimum mean return constraint, yield simple, mean-variance efficient optimal portfolio rules. In a market without the riskless asset, we obtain a closed-form portfolio rule that generalizes earlier results, without a minimum mean return restriction.
Open Access
Systemic risk measures based on value-at-risk
(2023-07) Al-Ali, Wissam
This thesis addresses the problem of computing systemic set-valued risk measures. The proposed method incorporates the clearing mechanism of the Eisenberg-Noe model, used as an aggregation function, with the value-at-risk, used as the underlying risk measure. The sample-average approximation (SAA) of the corresponding set-valued systemic risk measure can be calculated by solving a vector optimization problem. For this purpose, we propose a variation of the so-called grid algorithm in which grid points are evaluated by solving certain scalar mixed-integer programming problems, namely, the Pascoletti Serafini and norm-minimizing scalarizations. At the initialization step, we solve weighted sum scalarizations to establish a compact region for the algorithm to work on. We prove the convergence of the SAA optimal values of the scalarization problems to their respective true values. More-over, we prove the convergence of the approximated set-valued risk measure to the true set-valued risk measure in both the Wijsman and Hausdorff senses. In order to demonstrate the applicability of our findings, we construct a financial network based on the Bollob´as preferential attachment model. In addition, we model the economic disruptions using identically distributed random variables with a Pareto distribution. We conduct a comprehensive sensitivity analysis to investigate the effect of the number of scenarios, correlation coefficient, and Bollob´as network parameters on the systemic risk measure. The results highlight the minimal influence of the number of scenarios and correlation coefficient on the risk measure, demonstrating its stability and robustness, while shedding light on the profound significance of Bollob´as network parameters in determining the network dynamics and the overall level of systemic risk.