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Dynamic Semiparametric Models for Expected Shortfall (and Value-at-Risk)

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  • Andrew J. Patton
  • Johanna F. Ziegel
  • Rui Chen

Abstract

Expected Shortfall (ES) is the average return on a risky asset conditional on the return being below some quantile of its distribution, namely its Value-at-Risk (VaR). The Basel III Accord, which will be implemented in the years leading up to 2019, places new attention on ES, but unlike VaR, there is little existing work on modeling ES. We use recent results from statistical decision theory to overcome the problem of "elicitability" for ES by jointly modelling ES and VaR, and propose new dynamic models for these risk measures. We provide estimation and inference methods for the proposed models, and confirm via simulation studies that the methods have good finite-sample properties. We apply these models to daily returns on four international equity indices, and find the proposed new ES-VaR models outperform forecasts based on GARCH or rolling window models.

Suggested Citation

  • Andrew J. Patton & Johanna F. Ziegel & Rui Chen, 2017. "Dynamic Semiparametric Models for Expected Shortfall (and Value-at-Risk)," Papers 1707.05108, arXiv.org.
    • Handle: RePEc:arx:papers:1707.05108
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    JEL classification:

    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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