Journal of Financial Risk Management, 2021, 10, 367-395 https://www.scirp.org/journal/jfrm ISSN Online: 2167-9541 ISSN Print: 2167-9533 DOI: 10.4236/jfrm.2021.103021 Sep. 30, 2021 367 Journal of Financial Risk Management Modelling Stochastic Volatility in the Kenyan Securities Market Using Hidden Markov Models Matilda B. Bosire * , Samuel Chege Maina Strathmore University, Institute of Mathematical Sciences, Nairobi, Kenya Abstract This paper models stochastic volatility using Hidden Markov Models in Ken- ya. The univariate Stochastic volatility Model is calibrated to the Nairobi Se- curities Exchange 20 share index daily data from January 2012 to February 2021. The Hidden Markov model (HMM) is employed to establish volatility regimes while the Expected Maximization (EM) algorithm is applied in pa- rameter estimation. Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) techniques are employed in filtering out noisy observations in parameter estimation. The 4-state model, which divides the economy into pe- riods of very high, high, low, and very low volatility, is established to be op- timal. Keywords Hidden Markov Models, Stochastic Volatility, Nairobi Securities Exchange 20 (NSE 20) Share Index, Volatility Regimes 1. Introduction The probability that stock prices will rise or decline is an increasing function of volatility, which in turn leads to an increase in the value of options. The use of volatility as a proxy to risk has resulted in an increased need to accurately model and forecast volatility which is vital for a range of applications including finan- cial asset pricing, hedging strategies, portfolio selection and asset management. The Black-Scholes model, as a forerunner to the option pricing framework, is still widely used in the financial market. The model assumes that continuously compounded log spot asset prices are normally distributed with a constant mean and variance. However, empirical studies have shown that this is not always the case, as market prices have shown peakedness and fat tails, and the constant variance How to cite this paper: Bosire, M. B., & Maina, S. C. (2021). Modelling Stochastic Vo- latility in the Kenyan Securities Market Us- ing Hidden Markov Models. Journal of Fi- nancial Risk Management, 10, 367-395. https://doi.org/10.4236/jfrm.2021.103021 Received: July 30, 2021 Accepted: September 27, 2021 Published: September 30, 2021 Copyright © 2021 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access