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Modelling Kenyan Foreign Exchange Risk Using Asymmetry Garch Models and Extreme Value Theory Approaches

Received: 14 July 2018     Accepted: 17 August 2018     Published: 10 September 2018
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Abstract

The Foreign Exchange Market in developing countries, Kenya being one of them is a key driving force for the development of a country economic growth. In the last decade, world financial markets have been characterized by significant instabilities and the currency exchange rate market is not an exception. As a consequence of the significant instabilities in the financial markets, this paper models the tail risk associated with the Kenya Shilling against the leading currencies, especially the one day ahead Value-at-Risk forecast in risk control, by using the two leading alternatives, the two-stage GARCH-EVT approach and the asymmetry GARCH models. In practice by applying the conditional Extreme Value Theory, the tail behaviour of the daily returns is modelled and thus the VaR while by using the asymmetry GARCH models, one models the whole distribution of the returns and thereafter estimates the Value at Risk. In addition to modelling the value at risk, we further examine the performance of the two leading alternatives with the daily log returns of leading currencies in the Kenyan Foreign Exchange market (US dollar, Sterling Pound and Euro) foreign currencies from the period January 2005 – August 2017 for trading days excluding weekends and holidays. The backtesting result indicate that the conditional Extreme Value Theory does not completely dominate the asymmetry GARCH models in estimating the VaR especially in the Sterling Pound and Euro Exchange Rates.

Published in International Journal of Data Science and Analysis (Volume 4, Issue 3)
DOI 10.11648/j.ijdsa.20180403.11
Page(s) 38-45
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Asymmetry GARCH Models, Value-at-Risk, Extreme Value Theory and Backtesting

References
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[4] Glosten, Jagannathan and Runkel, "The Relationship between the expected value and volatility of nominal excess returns," Journal of Finance, vol. 48, pp. 1779-1801, 1993.
[5] Z. Ding, C. W. J and G. a. R. F. Engle, "A long memory property of stock market returns and a new model," Journal of empirical Finance, pp. 83-106, 1993.
[6] Engle, "Autoregressive Conditional Heteroscedasticty with estimates of variance of United Kingdom Inflation," Econometrica, pp. 987-1008, 1982.
[7] Bollerslev, "Generalized Autoregressive Condtional Heteroscedasticity," Journal of Econometrics, 1986.
[8] J. P. a. K. Bednarz-Okrzynska, "Application of Generalized Student’s T-Distribution In Modeling The Distribution of Empirical Return Rates on Selected Stock Exchange Indexes," The Journal of University of Szczecin, vol. 13, no. 2, p. 37, 2014.
[9] E. J. Gumbel, Statistics of Extremes, New York: Columbia University Press, 1958.
[10] A. A. Balkema and d. Haan, "Residual Life Time at Great Age," The Annals of Probability, vol. 2, no. 5, pp. 792-504, 1974.
[11] J. Picklands, "Statistical Inference Using Extreme Order Statistics," The Annals of Statistics, vol. 3, pp. 119-131, 1975.
[12] M. Alexander and Frey, "Estimation of Tail-Related Risk Measures for Heteroskedastic Financial Time Series: An Extreme Value Approach," Journal of Empirical Finance, vol. 7, pp. 271-300, 2000.
[13] P. Kupiec, "Techniques for Verifying the Accuracy of Risk Measurement Models," FEDS Paper, 1995.
[14] P. F. Christoffersen, "Evaluating Interval Forecasts," International Economic Review, vol. 39, pp. 841-862, 1998.
[15] Black, "Studies of Stock Price Volatility Changes," 1976.
[16] B. S. Hela, K. Adel and B. Makram, "Conditional VaR using GARCH-EVT approach:Forecasting Volatility in Tunisian Financial Market," Journal of Computations & Modelling,, pp. 95-115, 2012.
[17] Embrechts, Micosch and Kiaijppelberg, "Modelling Extremal Events for Insurance and Finance," Springer Verlag, Berlin, 1997.
[18] C. Omari, P. Mwita and A. Waititu, "Modelling USD/KES exchange rate volatility using GARCH models," IOSR Journal of Economics and Finance, vol. 8, pp. 15-26, 2017.
[19] Engle and Ng, "Measuring and testing the impact of news on volatility," 1993.
[20] L. Li, "A Comparative Study of GARCH and EVT models in Modeling Value-at-Risk (VaR)," 2017.
[21] Jorion, Value at Risk The New Benchmark for Managing Financial Risk, McGraw-Hill, 2001.
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Cite This Article
  • APA Style

    Mutua Kilai, Anthony Gichuhi Waititu, Anthony Wanjoya. (2018). Modelling Kenyan Foreign Exchange Risk Using Asymmetry Garch Models and Extreme Value Theory Approaches. International Journal of Data Science and Analysis, 4(3), 38-45. https://doi.org/10.11648/j.ijdsa.20180403.11

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    ACS Style

    Mutua Kilai; Anthony Gichuhi Waititu; Anthony Wanjoya. Modelling Kenyan Foreign Exchange Risk Using Asymmetry Garch Models and Extreme Value Theory Approaches. Int. J. Data Sci. Anal. 2018, 4(3), 38-45. doi: 10.11648/j.ijdsa.20180403.11

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    AMA Style

    Mutua Kilai, Anthony Gichuhi Waititu, Anthony Wanjoya. Modelling Kenyan Foreign Exchange Risk Using Asymmetry Garch Models and Extreme Value Theory Approaches. Int J Data Sci Anal. 2018;4(3):38-45. doi: 10.11648/j.ijdsa.20180403.11

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  • @article{10.11648/j.ijdsa.20180403.11,
      author = {Mutua Kilai and Anthony Gichuhi Waititu and Anthony Wanjoya},
      title = {Modelling Kenyan Foreign Exchange Risk Using Asymmetry Garch Models and Extreme Value Theory Approaches},
      journal = {International Journal of Data Science and Analysis},
      volume = {4},
      number = {3},
      pages = {38-45},
      doi = {10.11648/j.ijdsa.20180403.11},
      url = {https://doi.org/10.11648/j.ijdsa.20180403.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20180403.11},
      abstract = {The Foreign Exchange Market in developing countries, Kenya being one of them is a key driving force for the development of a country economic growth. In the last decade, world financial markets have been characterized by significant instabilities and the currency exchange rate market is not an exception. As a consequence of the significant instabilities in the financial markets, this paper models the tail risk associated with the Kenya Shilling against the leading currencies, especially the one day ahead Value-at-Risk forecast in risk control, by using the two leading alternatives, the two-stage GARCH-EVT approach and the asymmetry GARCH models. In practice by applying the conditional Extreme Value Theory, the tail behaviour of the daily returns is modelled and thus the VaR while by using the asymmetry GARCH models, one models the whole distribution of the returns and thereafter estimates the Value at Risk. In addition to modelling the value at risk, we further examine the performance of the two leading alternatives with the daily log returns of leading currencies in the Kenyan Foreign Exchange market (US dollar, Sterling Pound and Euro) foreign currencies from the period January 2005 – August 2017 for trading days excluding weekends and holidays. The backtesting result indicate that the conditional Extreme Value Theory does not completely dominate the asymmetry GARCH models in estimating the VaR especially in the Sterling Pound and Euro Exchange Rates.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - Modelling Kenyan Foreign Exchange Risk Using Asymmetry Garch Models and Extreme Value Theory Approaches
    AU  - Mutua Kilai
    AU  - Anthony Gichuhi Waititu
    AU  - Anthony Wanjoya
    Y1  - 2018/09/10
    PY  - 2018
    N1  - https://doi.org/10.11648/j.ijdsa.20180403.11
    DO  - 10.11648/j.ijdsa.20180403.11
    T2  - International Journal of Data Science and Analysis
    JF  - International Journal of Data Science and Analysis
    JO  - International Journal of Data Science and Analysis
    SP  - 38
    EP  - 45
    PB  - Science Publishing Group
    SN  - 2575-1891
    UR  - https://doi.org/10.11648/j.ijdsa.20180403.11
    AB  - The Foreign Exchange Market in developing countries, Kenya being one of them is a key driving force for the development of a country economic growth. In the last decade, world financial markets have been characterized by significant instabilities and the currency exchange rate market is not an exception. As a consequence of the significant instabilities in the financial markets, this paper models the tail risk associated with the Kenya Shilling against the leading currencies, especially the one day ahead Value-at-Risk forecast in risk control, by using the two leading alternatives, the two-stage GARCH-EVT approach and the asymmetry GARCH models. In practice by applying the conditional Extreme Value Theory, the tail behaviour of the daily returns is modelled and thus the VaR while by using the asymmetry GARCH models, one models the whole distribution of the returns and thereafter estimates the Value at Risk. In addition to modelling the value at risk, we further examine the performance of the two leading alternatives with the daily log returns of leading currencies in the Kenyan Foreign Exchange market (US dollar, Sterling Pound and Euro) foreign currencies from the period January 2005 – August 2017 for trading days excluding weekends and holidays. The backtesting result indicate that the conditional Extreme Value Theory does not completely dominate the asymmetry GARCH models in estimating the VaR especially in the Sterling Pound and Euro Exchange Rates.
    VL  - 4
    IS  - 3
    ER  - 

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Author Information
  • Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

  • Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

  • Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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