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Varying the VaR for Unconditional and Conditional Environments

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  • John Cotter
Abstract
Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from twelve European bourses, this paper presents VaR measures based on their unconditional and conditional distributions for single and multi-period settings. These measures underpinned by extreme value theory are statistically robust explicitly allowing for fat-tailed densities. Conditional tail estimates are obtained by adjusting the unconditional extreme value procedure with GARCH filtered returns. The conditional modelling results in iid returns allowing for the use of a simple and efficient multi-period extreme value scaling law. The paper examines the properties of these distinct conditional and unconditional trading models. The paper finds that the biases inherent in unconditional single and multi-period estimates assuming normality extend to the conditional setting.

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  • John Cotter, 2011. "Varying the VaR for Unconditional and Conditional Environments," Papers 1103.5649, arXiv.org.
    • Handle: RePEc:arx:papers:1103.5649
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    Cited by:

    1. Cotter, John & Dowd, Kevin, 2007. "The tail risks of FX return distributions: A comparison of the returns associated with limit orders and market orders," Finance Research Letters, Elsevier, vol. 4(3), pages 146-154, September.
    2. Karmakar, Madhusudan, 2013. "Estimation of tail-related risk measures in the Indian stock market: An extreme value approach," Review of Financial Economics, Elsevier, vol. 22(3), pages 79-85.
    3. John Cotter & Kevin Dowd, 2011. "Intra-Day Seasonality in Foreign Market Transactions," Working Papers 200744, Geary Institute, University College Dublin.
    4. Jouchi Nakajima & Tsuyoshi Kunihama & Yasuhiro Omori, 2017. "Bayesian modeling of dynamic extreme values: extension of generalized extreme value distributions with latent stochastic processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(7), pages 1248-1268, May.
    5. Psaradakis, Zacharias & Vávra, Marián, 2017. "A distance test of normality for a wide class of stationary processes," Econometrics and Statistics, Elsevier, vol. 2(C), pages 50-60.
    6. Aditya Banerjee & Samit Paul, 2024. "Idiosyncrasies of Intraday Risk in Emerging and Developed Markets: Efficacy of the MCS-GARCH Model and Extreme Value Theory," Global Business Review, International Management Institute, vol. 25(2), pages 468-490, April.
    7. Herrera, R. & Clements, A.E., 2018. "Point process models for extreme returns: Harnessing implied volatility," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 161-175.
    8. Candia, Claudio & Herrera, Rodrigo, 2024. "An empirical review of dynamic extreme value models for forecasting value at risk, expected shortfall and expectile," Journal of Empirical Finance, Elsevier, vol. 77(C).
    9. Kavussanos, Manolis G. & Dimitrakopoulos, Dimitris N., 2011. "Market risk model selection and medium-term risk with limited data: Application to ocean tanker freight markets," International Review of Financial Analysis, Elsevier, vol. 20(5), pages 258-268.
    10. Zacharias Psaradakis & Marian Vavra, 2017. "Normality Tests for Dependent Data," Working and Discussion Papers WP 12/2017, Research Department, National Bank of Slovakia.
    11. Karmakar, Madhusudan & Shukla, Girja K., 2015. "Managing extreme risk in some major stock markets: An extreme value approach," International Review of Economics & Finance, Elsevier, vol. 35(C), pages 1-25.
    12. Ra l de Jes s-Guti rrez & Roberto J. Santill n-Salgado, 2019. "Conditional Extreme Values Theory and Tail-related Risk Measures: Evidence from Latin American Stock Markets," International Journal of Economics and Financial Issues, Econjournals, vol. 9(3), pages 127-141.
    13. Madhusudan Karmakar, 2013. "Estimation of tail‐related risk measures in the Indian stock market: An extreme value approach," Review of Financial Economics, John Wiley & Sons, vol. 22(3), pages 79-85, September.
    14. Cotter, John & Dowd, Kevin, 2006. "Spectral Risk Measures with an Application to Futures Clearinghouse Variation Margin Requirements," MPRA Paper 3495, University Library of Munich, Germany.
    15. Samit Paul & Madhusudan Karmakar, 2017. "Relative Efficiency of Component GARCH-EVT Approach in Managing Intraday Market Risk," Multinational Finance Journal, Multinational Finance Journal, vol. 21(4), pages 247-283, December.
    16. Karmakar, Madhusudan & Paul, Samit, 2016. "Intraday risk management in International stock markets: A conditional EVT approach," International Review of Financial Analysis, Elsevier, vol. 44(C), pages 34-55.
    17. Wyn Morgan & John Cotter & Kevin Dowd, 2012. "Extreme Measures of Agricultural Financial Risk," Journal of Agricultural Economics, Wiley Blackwell, vol. 63(1), pages 65-82, February.
    18. Trenca Ioan & Zoicas-Ienciu Adrian, 2010. "The Correlation Between The Market Risk And The Liquidity Risk In The Romanian Banking Sector," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(1), pages 437-442, July.
    19. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    20. Christian Francq & Jean-Michel Zakoïan, 2013. "Estimating the Marginal Law of a Time Series With Applications to Heavy-Tailed Distributions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 412-425, October.
    21. Manel Youssef & Lotfi Belkacem & Khaled Mokni, 2015. "Extreme Value Theory and long-memory-GARCH Framework: Application to Stock Market," International Journal of Economics and Empirical Research (IJEER), The Economics and Social Development Organization (TESDO), vol. 3(8), pages 371-388, August.
    22. Juwon Seo, 2018. "Randomization Tests for Equality in Dependence Structure," Papers 1811.02105, arXiv.org.

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    JEL classification:

    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G0 - Financial Economics - - General

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