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Jumping VaR: Order Statistics Volatility Estimator for Jumps Classification and Market Risk Modeling

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Listed:
  • Luca Spadafora
  • Francesca Sivero
  • Nicola Picchiotti

Abstract

This paper proposes a new integrated variance estimator based on order statistics within the framework of jump-diffusion models. Its ability to disentangle the integrated variance from the total process quadratic variation is confirmed by both simulated and empirical tests. For practical purposes, we introduce an iterative algorithm to estimate the time-varying volatility and the occurred jumps of log-return time series. Such estimates enable the definition of a new market risk model for the Value at Risk forecasting. We show empirically that this procedure outperforms the standard historical simulation method applying standard back-testing approach.

Suggested Citation

  • Luca Spadafora & Francesca Sivero & Nicola Picchiotti, 2018. "Jumping VaR: Order Statistics Volatility Estimator for Jumps Classification and Market Risk Modeling," Papers 1803.07021, arXiv.org, revised Mar 2018.
    • Handle: RePEc:arx:papers:1803.07021
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    References listed on IDEAS

    as
    1. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37.
    2. Jos'e E. Figueroa-L'opez & Cecilia Mancini, 2017. "Optimum thresholding using mean and conditional mean square error," Papers 1708.04339, arXiv.org.
    3. Luca Spadafora & Gennady P Berman, 2017. "Theoretical Foundations for Quantitative Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10326, February.
    4. Cecilia Mancini, 2010. "Speed of convergence of the threshold estimator of integrated variance," Working Papers - Mathematical Economics 2010-03, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
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