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Multifractality and value-at-risk forecasting of exchange rates

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  • Batten, Jonathan A.
  • Kinateder, Harald
  • Wagner, Niklas

Abstract

This paper addresses market risk prediction for high frequency foreign exchange rates under nonlinear risk scaling behaviour. We use a modified version of the multifractal model of asset returns (MMAR) where trading time is represented by the series of volume ticks. Our dataset consists of 138,418 5-min round-the-clock observations of EUR/USD spot quotes and trading ticks during the period January 5, 2006 to December 31, 2007. Considering fat-tails, long-range dependence as well as scale inconsistency with the MMAR, we derive out-of-sample value-at-risk (VaR) forecasts and compare our approach to historical simulation as well as a benchmark GARCH(1,1) location-scale VaR model. Our findings underline that the multifractal properties in EUR/USD returns in fact have notable risk management implications. The MMAR approach is a parsimonious model which produces admissible VaR forecasts at the 12-h forecast horizon. For the daily horizon, the MMAR outperforms both alternatives based on conditional as well as unconditional coverage statistics.

Suggested Citation

  • Batten, Jonathan A. & Kinateder, Harald & Wagner, Niklas, 2014. "Multifractality and value-at-risk forecasting of exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 71-81.
  • Handle: RePEc:eee:phsmap:v:401:y:2014:i:c:p:71-81
    DOI: 10.1016/j.physa.2014.01.024
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    References listed on IDEAS

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    Cited by:

    1. Samet Günay, 2016. "Performance of the Multifractal Model of Asset Returns (MMAR): Evidence from Emerging Stock Markets," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 4(2), pages 1-17, May.
    2. Alam, Nafis & Arshad, Shaista & Rizvi, Syed Aun R., 2016. "Do Islamic stock indices perform better than conventional counterparts? An empirical investigation of sectoral efficiency," Review of Financial Economics, Elsevier, vol. 31(C), pages 108-114.
    3. Dewandaru, Ginanjar & Masih, Rumi & Bacha, Obiyathulla Ismath & Masih, A. Mansur. M., 2015. "Developing trading strategies based on fractal finance: An application of MF-DFA in the context of Islamic equities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 223-235.
    4. Auer, Benjamin R., 2016. "On time-varying predictability of emerging stock market returns," Emerging Markets Review, Elsevier, vol. 27(C), pages 1-13.
    5. Zhang, Bangzheng & Wei, Yu & Yu, Jiang & Lai, Xiaodong & Peng, Zhenfeng, 2014. "Forecasting VaR and ES of stock index portfolio: A Vine copula method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 112-124.
    6. Gong, Pu & Weng, Yingliang, 2016. "Value-at-Risk forecasts by a spatiotemporal model in Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 441(C), pages 173-191.
    7. Lee, Hojin & Song, Jae Wook & Chang, Woojin, 2016. "Multifractal Value at Risk model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 113-122.

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