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

Mutua Kilai; Anthony Gichuhi Waititu; Anthony Wanjoya

doi:doi:10.11648/j.ijdsa.20180403.11

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

Mutua Kilai, Anthony Gichuhi Waititu, Anthony Wanjoya

Published in International Journal of Data Science and Analysis (Volume 4, Issue 3)

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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[13]	P. Kupiec, "Techniques for Verifying the Accuracy of Risk Measurement Models," FEDS Paper, 1995.
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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

Mutua Kilai

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Gichuhi Waititu

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

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

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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}
}

Copy | Download

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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