Modelling the Volatility of Central Bank of Kenya Currency Exchange Rates

Oganga Caneble; Anthony Wanjoya; Anthony Ngunyi

doi:doi:10.11648/j.ijdst.20210703.13

| Peer-Reviewed

Modelling the Volatility of Central Bank of Kenya Currency Exchange Rates

Oganga Caneble, Anthony Wanjoya, Anthony Ngunyi

Published in International Journal on Data Science and Technology (Volume 7, Issue 3)

Received: 15 August 2021 Accepted: 25 August 2021 Published: 4 September 2021

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In emerging countries, such as Kenya, the foreign exchange market is an important aspect in the economic development of a country. The currency exchange rate market, like the rest of the world's financial markets, has been marked by considerable instabilities over the last decade. The objective of this paper is to model the volatility of the KSH/USD exchange rate prices using and calculate the VaR using the GARCH-EVT model. In particular, this article uses the two-stage GARCH-EVT approach to estimate the value at risk of the Kenyan Shilling against the US dollar., particularly the one-day ahead Value-at-Risk forecast in risk control. The conditional and unconditional coverage test are used to back test the model. We compare the performance of the GARCH-EVT with the daily log returns of key currency in addition to modelling the value at risk in the Kenyan Foreign Exchange market (US dollar) foreign currencies from the period November 2004 – June 2021 for trading days with the exception of holidays and weekends. The mean equation that was best fitting for the data was ARMA (4,2). The optimal GARCH model for the returns of the KSH/USD exchange rate is the GARCH (1,3) with student-t innovations. The results of the backtesting show that GARCH-EVT can be utilized to estimate and forecast VaR at both 5% and 1% level of significance.

Published in	International Journal on Data Science and Technology (Volume 7, Issue 3)
DOI	10.11648/j.ijdst.20210703.13
Page(s)	62-68
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), 2021. Published by Science Publishing Group

Keywords

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

References

[1]	P. Jorion, Value At Risk: The New Benchmark for managing Financial Risk, 2006.
[2]	Jorion, Value at Risk The New Benchmark for Managing Financial Risk, McGraw-Hill, 2001.
[3]	S. Omar, "GARCH modeling in monthly foreign exchange and share prices for specificcompanies in Kenya.," American Journal of Mathematics and Applications, vol. I, pp. 5-12, 2013.
[4]	R. T. Kipkoech, "Modeling volatility under normal and student-t distributional assumptions (a case study of the Kenyan exchange rates)," American Journal of Applied Mathematics and Statistics, pp. 179-184, 2014.
[5]	A. A. Adepoju, O. S. Yaya and O. O. Ojo, "Estimation of Garch models for Nigerian Exchange rates under non-Gaussian innovations," 2013.
[6]	I. Maana, P. N. Mwita and R. Odhiambo., "Modelling the volatility of exchange rates in the Kenyan market," African Journal of Business Management, 2010.
[7]	Bollerslev, "Generalized Autoregressive Condtional Heteroscedasticity," Journal of Econometrics, 1986.
[8]	Y. Lan, K. Chokethaworn and C. Chaiboonsri., "Forecasting Chinese Yuan currency risk with extreme value theory," 2014.
[9]	J. de Dieu Ntawihebasenga, J. K. Mung’atu and P. N. Mwita, "Modeling the volatility of exchange rates in Rwandese markets.," American Journal of Theoretical and Applied Statistics, 2015.
[10]	I. aana, A. Kamau and K. Kisinguh, "Modelling extreme volatility in the daily exchange rates of the Kenya shilling against the US dollar," Journal of Economics and International Finance, 2015.
[11]	Engle, "Autoregressive Conditional Heteroscedasticty with estimates of variance of United Kingdom Inflation," Econometrica, pp. 987-1008, 1982.
[12]	E. J. Gumbel, Statistics of Extremes, New York: Columbia University Press, 1958.
[13]	A. A. Balkema and d. Haan, "Residual Life Time at Great Age," The Annals of Probability, vol. 2, no. 5, pp. 792-504, 1974.
[14]	J. Picklands, "Statistical Inference Using Extreme Order Statistics," The Annals of Statistics, vol. 3, pp. 119-131, 1975.
[15]	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.
[16]	P. Kupiec, "Techniques for Verifying the Accuracy of Risk Measurement Models," FEDS Paper, 1995.
[17]	P. F. Christoffersen, "Evaluating Interval Forecasts," International Economic Review, vol. 39, pp. 841-862, 1998.

Cite This Article

Plain Text BibTeX RIS

APA Style

Oganga Caneble, Anthony Wanjoya, Anthony Ngunyi. (2021). Modelling the Volatility of Central Bank of Kenya Currency Exchange Rates. International Journal on Data Science and Technology, 7(3), 62-68. https://doi.org/10.11648/j.ijdst.20210703.13

Copy | Download

ACS Style

Oganga Caneble; Anthony Wanjoya; Anthony Ngunyi. Modelling the Volatility of Central Bank of Kenya Currency Exchange Rates. Int. J. Data Sci. Technol. 2021, 7(3), 62-68. doi: 10.11648/j.ijdst.20210703.13

Copy | Download

AMA Style

Oganga Caneble, Anthony Wanjoya, Anthony Ngunyi. Modelling the Volatility of Central Bank of Kenya Currency Exchange Rates. Int J Data Sci Technol. 2021;7(3):62-68. doi: 10.11648/j.ijdst.20210703.13

Copy | Download

@article{10.11648/j.ijdst.20210703.13,
  author = {Oganga Caneble and Anthony Wanjoya and Anthony Ngunyi},
  title = {Modelling the Volatility of Central Bank of Kenya Currency Exchange Rates},
  journal = {International Journal on Data Science and Technology},
  volume = {7},
  number = {3},
  pages = {62-68},
  doi = {10.11648/j.ijdst.20210703.13},
  url = {https://doi.org/10.11648/j.ijdst.20210703.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdst.20210703.13},
  abstract = {In emerging countries, such as Kenya, the foreign exchange market is an important aspect in the economic development of a country. The currency exchange rate market, like the rest of the world's financial markets, has been marked by considerable instabilities over the last decade. The objective of this paper is to model the volatility of the KSH/USD exchange rate prices using and calculate the VaR using the GARCH-EVT model. In particular, this article uses the two-stage GARCH-EVT approach to estimate the value at risk of the Kenyan Shilling against the US dollar., particularly the one-day ahead Value-at-Risk forecast in risk control. The conditional and unconditional coverage test are used to back test the model. We compare the performance of the GARCH-EVT with the daily log returns of key currency in addition to modelling the value at risk in the Kenyan Foreign Exchange market (US dollar) foreign currencies from the period November 2004 – June 2021 for trading days with the exception of holidays and weekends. The mean equation that was best fitting for the data was ARMA (4,2). The optimal GARCH model for the returns of the KSH/USD exchange rate is the GARCH (1,3) with student-t innovations. The results of the backtesting show that GARCH-EVT can be utilized to estimate and forecast VaR at both 5% and 1% level of significance.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Modelling the Volatility of Central Bank of Kenya Currency Exchange Rates
AU  - Oganga Caneble
AU  - Anthony Wanjoya
AU  - Anthony Ngunyi
Y1  - 2021/09/04
PY  - 2021
N1  - https://doi.org/10.11648/j.ijdst.20210703.13
DO  - 10.11648/j.ijdst.20210703.13
T2  - International Journal on Data Science and Technology
JF  - International Journal on Data Science and Technology
JO  - International Journal on Data Science and Technology
SP  - 62
EP  - 68
PB  - Science Publishing Group
SN  - 2472-2235
UR  - https://doi.org/10.11648/j.ijdst.20210703.13
AB  - In emerging countries, such as Kenya, the foreign exchange market is an important aspect in the economic development of a country. The currency exchange rate market, like the rest of the world's financial markets, has been marked by considerable instabilities over the last decade. The objective of this paper is to model the volatility of the KSH/USD exchange rate prices using and calculate the VaR using the GARCH-EVT model. In particular, this article uses the two-stage GARCH-EVT approach to estimate the value at risk of the Kenyan Shilling against the US dollar., particularly the one-day ahead Value-at-Risk forecast in risk control. The conditional and unconditional coverage test are used to back test the model. We compare the performance of the GARCH-EVT with the daily log returns of key currency in addition to modelling the value at risk in the Kenyan Foreign Exchange market (US dollar) foreign currencies from the period November 2004 – June 2021 for trading days with the exception of holidays and weekends. The mean equation that was best fitting for the data was ARMA (4,2). The optimal GARCH model for the returns of the KSH/USD exchange rate is the GARCH (1,3) with student-t innovations. The results of the backtesting show that GARCH-EVT can be utilized to estimate and forecast VaR at both 5% and 1% level of significance.
VL  - 7
IS  - 3
ER  -

Copy | Download

Author Information

Oganga Caneble

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
Anthony Ngunyi

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Oganga Caneble, Anthony Wanjoya, Anthony Ngunyi. (2021). Modelling the Volatility of Central Bank of Kenya Currency Exchange Rates. International Journal on Data Science and Technology, 7(3), 62-68. https://doi.org/10.11648/j.ijdst.20210703.13

Copy | Download

ACS Style

Oganga Caneble; Anthony Wanjoya; Anthony Ngunyi. Modelling the Volatility of Central Bank of Kenya Currency Exchange Rates. Int. J. Data Sci. Technol. 2021, 7(3), 62-68. doi: 10.11648/j.ijdst.20210703.13

Copy | Download

AMA Style

Oganga Caneble, Anthony Wanjoya, Anthony Ngunyi. Modelling the Volatility of Central Bank of Kenya Currency Exchange Rates. Int J Data Sci Technol. 2021;7(3):62-68. doi: 10.11648/j.ijdst.20210703.13

Copy | Download

@article{10.11648/j.ijdst.20210703.13,
  author = {Oganga Caneble and Anthony Wanjoya and Anthony Ngunyi},
  title = {Modelling the Volatility of Central Bank of Kenya Currency Exchange Rates},
  journal = {International Journal on Data Science and Technology},
  volume = {7},
  number = {3},
  pages = {62-68},
  doi = {10.11648/j.ijdst.20210703.13},
  url = {https://doi.org/10.11648/j.ijdst.20210703.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdst.20210703.13},
  abstract = {In emerging countries, such as Kenya, the foreign exchange market is an important aspect in the economic development of a country. The currency exchange rate market, like the rest of the world's financial markets, has been marked by considerable instabilities over the last decade. The objective of this paper is to model the volatility of the KSH/USD exchange rate prices using and calculate the VaR using the GARCH-EVT model. In particular, this article uses the two-stage GARCH-EVT approach to estimate the value at risk of the Kenyan Shilling against the US dollar., particularly the one-day ahead Value-at-Risk forecast in risk control. The conditional and unconditional coverage test are used to back test the model. We compare the performance of the GARCH-EVT with the daily log returns of key currency in addition to modelling the value at risk in the Kenyan Foreign Exchange market (US dollar) foreign currencies from the period November 2004 – June 2021 for trading days with the exception of holidays and weekends. The mean equation that was best fitting for the data was ARMA (4,2). The optimal GARCH model for the returns of the KSH/USD exchange rate is the GARCH (1,3) with student-t innovations. The results of the backtesting show that GARCH-EVT can be utilized to estimate and forecast VaR at both 5% and 1% level of significance.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Modelling the Volatility of Central Bank of Kenya Currency Exchange Rates
AU  - Oganga Caneble
AU  - Anthony Wanjoya
AU  - Anthony Ngunyi
Y1  - 2021/09/04
PY  - 2021
N1  - https://doi.org/10.11648/j.ijdst.20210703.13
DO  - 10.11648/j.ijdst.20210703.13
T2  - International Journal on Data Science and Technology
JF  - International Journal on Data Science and Technology
JO  - International Journal on Data Science and Technology
SP  - 62
EP  - 68
PB  - Science Publishing Group
SN  - 2472-2235
UR  - https://doi.org/10.11648/j.ijdst.20210703.13
AB  - In emerging countries, such as Kenya, the foreign exchange market is an important aspect in the economic development of a country. The currency exchange rate market, like the rest of the world's financial markets, has been marked by considerable instabilities over the last decade. The objective of this paper is to model the volatility of the KSH/USD exchange rate prices using and calculate the VaR using the GARCH-EVT model. In particular, this article uses the two-stage GARCH-EVT approach to estimate the value at risk of the Kenyan Shilling against the US dollar., particularly the one-day ahead Value-at-Risk forecast in risk control. The conditional and unconditional coverage test are used to back test the model. We compare the performance of the GARCH-EVT with the daily log returns of key currency in addition to modelling the value at risk in the Kenyan Foreign Exchange market (US dollar) foreign currencies from the period November 2004 – June 2021 for trading days with the exception of holidays and weekends. The mean equation that was best fitting for the data was ARMA (4,2). The optimal GARCH model for the returns of the KSH/USD exchange rate is the GARCH (1,3) with student-t innovations. The results of the backtesting show that GARCH-EVT can be utilized to estimate and forecast VaR at both 5% and 1% level of significance.
VL  - 7
IS  - 3
ER  -

Copy | Download