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Estimation of Distortion Risk Measures

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  • Hideatsu Tsukahara

Abstract

For the class of distortion risk measures, a natural estimator has the form of L-statistics. In this article, we investigate the large sample properties of general L-statistics based on weakly dependent data and apply them to our estimator. Under certain regularity conditions, which are somewhat weaker than the ones found in the literature, we prove that the estimator is strongly consistent and asymptotically normal. Furthermore, we give a consistent estimator for its asymptotic variance using spectral density estimators of a related stationary sequence. The behavior of the estimator is examined using simulation in two examples: inverse-gamma autoregressive stochastic volatility model and GARCH(1,1).

Suggested Citation

  • Hideatsu Tsukahara, 2014. "Estimation of Distortion Risk Measures," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 213-235.
    • Handle: RePEc:oup:jfinec:v:12:y:2014:i:1:p:213-235.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbt005
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    Cited by:

    1. Matthias Fischer & Thorsten Moser & Marius Pfeuffer, 2018. "A Discussion on Recent Risk Measures with Application to Credit Risk: Calculating Risk Contributions and Identifying Risk Concentrations," Risks, MDPI, vol. 6(4), pages 1-28, December.

    More about this item

    Keywords

    risk measure; distortion; consistency; asymptotic normality; asymptotic variance estimation; stochastic volatility;
    All these keywords.

    JEL classification:

    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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