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A Stochastic Dominance Approach to Financial Risk Management Strategies

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Abstract

The Basel III Accord requires that banks and other Authorized Deposit-taking Institutions (ADIs) communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one of a range of alternative risk models to forecast Value-at-Risk (VaR). The risk estimates from these models are used to determine the daily capital charges (DCC) and associated capital costs of ADIs, depending in part on the number of previous violations, whereby realized losses exceed the estimated VaR. In this paper we define risk management in terms of choosing sensibly from a variety of risk models and discuss the optimal selection of financial risk models. A previous approach to model selection for predicting VaR proposed combining alternative risk models and ranking such models on the basis of average DCC. This method is based only on the first moment of the DCC distribution, supported by a restrictive evaluation function. In this paper, we consider uniform rankings of models over large classes of evaluation functions that may reflect different weights and concerns over different intervals of the distribution of losses and DCC. The uniform rankings are based on recently developed statistical tests of stochastic dominance (SD). The SD tests are illustrated using the prices and returns of VIX futures. The empirical findings show that the tests of SD can rank different pairs of models to a statistical degree of confidence, and that the alternative (recentered) SD tests are in general agreement.

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  • Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Esfandiar Maasoumi & Teodosio Pérez Amaral, 2014. "A Stochastic Dominance Approach to Financial Risk Management Strategies," Documentos de Trabajo del ICAE 2014-08, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised Apr 2014.
  • Handle: RePEc:ucm:doicae:1408
    Note: The authors are most grateful to Michael McAleer for many comments and suggestions. For financial support, the first author wishes to thank the National Science Council, Taiwan, and the second and fourth authors acknowledge the Ministerio de Economía y Competitividad and Comunidad de Madrid, Spain.
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    2. Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Esfandiar Maasoumi & Michael McAleer & Teodosio Pérez-Amaral, 2015. "A Stochastic Dominance Approach to the Basel III Dilemma: Expected Shortfall or VaR?," Documentos de Trabajo del ICAE 2015-16, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    3. Chang, Chia-Lin & McAleer, Michael, 2015. "Econometric analysis of financial derivatives: An overview," Journal of Econometrics, Elsevier, vol. 187(2), pages 403-407.
    4. Chang, C-L. & McAleer, M.J., 2014. "Econometric Analysis of Financial Derivatives," Econometric Institute Research Papers EI 2015-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Cerqueti, Roy & Giacalone, Massimiliano & Panarello, Demetrio, 2019. "A Generalized Error Distribution Copula-based method for portfolios risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 687-695.

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    More about this item

    Keywords

    Stochastic dominance; Value-at-Risk; daily capital charges; violation penalties; optimizing strategy; Basel III Accord; VIX futures; global financial crisis.;
    All these keywords.

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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