Extreme Values Modelling of Nairobi Securities Exchange Index

Kelvin Ambrose Kiragu; Joseph Kyalo Mung’atu

doi:doi:10.11648/j.ajtas.20160504.20

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Extreme Values Modelling of Nairobi Securities Exchange Index

Kelvin Ambrose Kiragu, Joseph Kyalo Mung’atu

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 4)

Received: 21 June 2016 Accepted: 28 June 2016 Published: 13 July 2016

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Abstract

Extreme events and the clustering of extreme values provide fundamental information which can be used for risk assessment in finance. When applying extreme value analysis to financial time series we handle two major issues, bias and serial dependence. The main objective of the study will be to model the extreme values of the NSE all share index using EVT method thus contributing to empirical evidence of the research into the behavior of the extreme returns of financial series in East Africa and specifically Kenya. This study will model the extreme values of the Nairobi Securities Exchange all share index (2008-2015) by applying the Extreme Value Theory to fit a model to the tails of the daily stock returns data. A GARCH-type model will be fitted to the data to correct for the effects of autocorrelation and conditional heteroscedasticity before the EVT method is applied. The Peak-Over-Threshold approach will be employed with the model parameters obtained by means of Maximum Likelihood Estimation. The models goodness of fit will be assessed graphically using Q-Q and density plots.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 4)
DOI	10.11648/j.ajtas.20160504.20
Page(s)	234-241
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), 2024. Published by Science Publishing Group

Keywords

Extreme Value Theory (EVT), Generalized Pareto Distribution (GPD), Peaks-Over-Threshold (POT), Nairobi Securities Exchange (NSE), NSE All Share Index (NASI)

References

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[2]	B. V. Gnedenko, ‘Sur la distribution limite du terme d’une serie aleatoire’, Annals of Mathematics, 44, 1943, pp. 423-453.
[3]	P. Embrechts, C. Kluppelberg and T. Mikosch, ‘Modelling extremal events for insurance and finance’, Springer-Verlag, Berlin, 1997.
[4]	D. M. Mason, ‘Laws of large numbers for sums of extreme values’, Annals of Probability, Vol 10, No 3, 1982, pp. 754-764.
[5]	F. Ren and D. E. Giles, ‘Extreme value analysis of daily Canadian crude oil prices’, Econometrics Working Paper, EWP 0708. University of Victoria, 2007.
[6]	A. J. McNeil and R. Frey, ‘Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach’, Journal of Empirical Finance 7, 2000, pp. 271-300.
[7]	J. Pickands, ‘Statistical inference using extreme order statistics’, Annals of Statistics, 3, 1975, pp. 119-131.
[8]	A. Balkema and L. deHaan, ‘Residual lifetime at great age’, Annals of Probability, 2, 1974, pp. 792-804.
[9]	E. N. Nortey, K. Asare and O. Mettle, ‘Extreme value modelling of Ghana stock exchange index’, Springer plus 2015, Department of statistics, University of Ghana.
[10]	D. A. Polakow and A. J. Seymour, ‘A coupling of extreme-value theory and volatility updating with value-at-risk estimation in emerging markets’, South African test. Multinational Finance Journal, 7, 2003, pp. 3-23.
[11]	V. Djakovic, G. Andjelic and J. Borocki, ‘Performance of extreme value theory in emerging markets: An empirical treatment’, African Journal of Business Management, Vol 5 (2), 2011, pp. 340-369.
[12]	G. Bi, & D. Giles, ‘An application of extreme value analysis to U.S. movie box office returns’, Econometrics Working Paper EWP 0705, 2007.
[13]	R. Gencay and F. Selcuk, ‘Extreme value theory and value-at-risk: Relative performance in emerging markets’, International Journal of Forecasting, Vol 20 (2), 2004, pp. 287-303.
[14]	T. Krehbiel and L. C. Adkins, ‘Price risk in the nymex energy complex: An extreme value approach’, Journal of Future Mark, 25, 2005, pp. 309-337.
[15]	J. Cerovic, M. Lipovina-Bozovic and S. Vujosevic, ‘A comparative analysis of value at risk measurement on emerging stock markets: Montenegro case’, Business Systems Research Journal, Vol 6 (1), 2015, pp. 36-55.
[16]	P. I. Louangrath, ‘Stock price analysis under extreme value theory’, Bangkok University International College, Thailand, 2016.
[17]	J. W. M. Mwamba, S. Hammoudeh and R. Gupta, ‘Financial tail risks and the shapes of the extreme value distribution: A comparison between conventional and sharia-compliant stock indexes’, University of Pretoria Department of Economics Working Paper Series No. 201480, 2014.
[18]	A. J. McNeil and R. Frey, ‘Estimation of Tail-related Risk Measures for Heteroscedastic Financial Time Series: an extreme value approach’, Journal of Empirical Finance 7, 2000, pp. 271-300.

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APA Style

Kelvin Ambrose Kiragu, Joseph Kyalo Mung’atu. (2016). Extreme Values Modelling of Nairobi Securities Exchange Index. American Journal of Theoretical and Applied Statistics, 5(4), 234-241. https://doi.org/10.11648/j.ajtas.20160504.20

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ACS Style

Kelvin Ambrose Kiragu; Joseph Kyalo Mung’atu. Extreme Values Modelling of Nairobi Securities Exchange Index. Am. J. Theor. Appl. Stat. 2016, 5(4), 234-241. doi: 10.11648/j.ajtas.20160504.20

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AMA Style

Kelvin Ambrose Kiragu, Joseph Kyalo Mung’atu. Extreme Values Modelling of Nairobi Securities Exchange Index. Am J Theor Appl Stat. 2016;5(4):234-241. doi: 10.11648/j.ajtas.20160504.20

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@article{10.11648/j.ajtas.20160504.20,
  author = {Kelvin Ambrose Kiragu and Joseph Kyalo Mung’atu},
  title = {Extreme Values Modelling of Nairobi Securities Exchange Index},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {4},
  pages = {234-241},
  doi = {10.11648/j.ajtas.20160504.20},
  url = {https://doi.org/10.11648/j.ajtas.20160504.20},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160504.20},
  abstract = {Extreme events and the clustering of extreme values provide fundamental information which can be used for risk assessment in finance. When applying extreme value analysis to financial time series we handle two major issues, bias and serial dependence. The main objective of the study will be to model the extreme values of the NSE all share index using EVT method thus contributing to empirical evidence of the research into the behavior of the extreme returns of financial series in East Africa and specifically Kenya. This study will model the extreme values of the Nairobi Securities Exchange all share index (2008-2015) by applying the Extreme Value Theory to fit a model to the tails of the daily stock returns data. A GARCH-type model will be fitted to the data to correct for the effects of autocorrelation and conditional heteroscedasticity before the EVT method is applied. The Peak-Over-Threshold approach will be employed with the model parameters obtained by means of Maximum Likelihood Estimation. The models goodness of fit will be assessed graphically using Q-Q and density plots.},
 year = {2016}
}

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TY  - JOUR
T1  - Extreme Values Modelling of Nairobi Securities Exchange Index
AU  - Kelvin Ambrose Kiragu
AU  - Joseph Kyalo Mung’atu
Y1  - 2016/07/13
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160504.20
DO  - 10.11648/j.ajtas.20160504.20
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 234
EP  - 241
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160504.20
AB  - Extreme events and the clustering of extreme values provide fundamental information which can be used for risk assessment in finance. When applying extreme value analysis to financial time series we handle two major issues, bias and serial dependence. The main objective of the study will be to model the extreme values of the NSE all share index using EVT method thus contributing to empirical evidence of the research into the behavior of the extreme returns of financial series in East Africa and specifically Kenya. This study will model the extreme values of the Nairobi Securities Exchange all share index (2008-2015) by applying the Extreme Value Theory to fit a model to the tails of the daily stock returns data. A GARCH-type model will be fitted to the data to correct for the effects of autocorrelation and conditional heteroscedasticity before the EVT method is applied. The Peak-Over-Threshold approach will be employed with the model parameters obtained by means of Maximum Likelihood Estimation. The models goodness of fit will be assessed graphically using Q-Q and density plots.
VL  - 5
IS  - 4
ER  -

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Author Information

Kelvin Ambrose Kiragu

Applied Statistics, Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Joseph Kyalo Mung’atu

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

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APA Style

Kelvin Ambrose Kiragu, Joseph Kyalo Mung’atu. (2016). Extreme Values Modelling of Nairobi Securities Exchange Index. American Journal of Theoretical and Applied Statistics, 5(4), 234-241. https://doi.org/10.11648/j.ajtas.20160504.20

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ACS Style

Kelvin Ambrose Kiragu; Joseph Kyalo Mung’atu. Extreme Values Modelling of Nairobi Securities Exchange Index. Am. J. Theor. Appl. Stat. 2016, 5(4), 234-241. doi: 10.11648/j.ajtas.20160504.20

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AMA Style

Kelvin Ambrose Kiragu, Joseph Kyalo Mung’atu. Extreme Values Modelling of Nairobi Securities Exchange Index. Am J Theor Appl Stat. 2016;5(4):234-241. doi: 10.11648/j.ajtas.20160504.20

Copy | Download

@article{10.11648/j.ajtas.20160504.20,
  author = {Kelvin Ambrose Kiragu and Joseph Kyalo Mung’atu},
  title = {Extreme Values Modelling of Nairobi Securities Exchange Index},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {4},
  pages = {234-241},
  doi = {10.11648/j.ajtas.20160504.20},
  url = {https://doi.org/10.11648/j.ajtas.20160504.20},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160504.20},
  abstract = {Extreme events and the clustering of extreme values provide fundamental information which can be used for risk assessment in finance. When applying extreme value analysis to financial time series we handle two major issues, bias and serial dependence. The main objective of the study will be to model the extreme values of the NSE all share index using EVT method thus contributing to empirical evidence of the research into the behavior of the extreme returns of financial series in East Africa and specifically Kenya. This study will model the extreme values of the Nairobi Securities Exchange all share index (2008-2015) by applying the Extreme Value Theory to fit a model to the tails of the daily stock returns data. A GARCH-type model will be fitted to the data to correct for the effects of autocorrelation and conditional heteroscedasticity before the EVT method is applied. The Peak-Over-Threshold approach will be employed with the model parameters obtained by means of Maximum Likelihood Estimation. The models goodness of fit will be assessed graphically using Q-Q and density plots.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Extreme Values Modelling of Nairobi Securities Exchange Index
AU  - Kelvin Ambrose Kiragu
AU  - Joseph Kyalo Mung’atu
Y1  - 2016/07/13
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160504.20
DO  - 10.11648/j.ajtas.20160504.20
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 234
EP  - 241
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160504.20
AB  - Extreme events and the clustering of extreme values provide fundamental information which can be used for risk assessment in finance. When applying extreme value analysis to financial time series we handle two major issues, bias and serial dependence. The main objective of the study will be to model the extreme values of the NSE all share index using EVT method thus contributing to empirical evidence of the research into the behavior of the extreme returns of financial series in East Africa and specifically Kenya. This study will model the extreme values of the Nairobi Securities Exchange all share index (2008-2015) by applying the Extreme Value Theory to fit a model to the tails of the daily stock returns data. A GARCH-type model will be fitted to the data to correct for the effects of autocorrelation and conditional heteroscedasticity before the EVT method is applied. The Peak-Over-Threshold approach will be employed with the model parameters obtained by means of Maximum Likelihood Estimation. The models goodness of fit will be assessed graphically using Q-Q and density plots.
VL  - 5
IS  - 4
ER  -

Copy | Download