Browsing by Author "Mwaniki, Joseph I"

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    On regime-switching European option pricing
    (Taylor & Francis, 2023) Simwa, Richard O; Mwaniki, Joseph I; Kalovwe, Sebastian K
    The concern of this article is to derive a regime switching model that can be utilized to price European call options for a financial market that exhibits structural changes with time. The model is formulated based on the fact that the underlying asset process is described by a geometric Brownian motion that is modulated by a continuous-time Markov chain with two regimes. Moreover, by an application of the change of measure technique, an option price is derived under the risk neutral valuation and the model parameter estimates is performed by use of the maximum likelihood estimation. The model implementation is carried out by utilizing the Russell 2000 and Facebook in dices data sets. The model results are compared with that of the Black-Scholes model in order to establish the model with better results in terms of predicting the European call option prices. In general, the data sets have common characteristics of financial time series across the regimes and the volatility process spends longer time in regime 2 than it stays in regime 1. The predicted call option prices from both models are more or less similar across the market indices; however, the results of the Black-Scholes model are a bit closer to the market prices than that of the regime-switching model across the two markets. Therefore, the Black-Scholes model slightly gives better results for the Russell 2000 and Facebook indices data sets as compared with the RS model.
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    On stock returns volatility and trading volume of the Nairobi securities exchange index
    (RMS: Research in Mathematics &Statistics, 2021) Simwa, Richard O; Mwaniki, Joseph I; Kalovwe, Sebastian K
    This study attempts to put forward a framework that can be utilized to model the dynamics of the underlying returns on asset. The intention is to probe the dynamic connection between volatility of stock returns and trading volume of the Nairobi Securities Exchange (NSE20) index. The consequence of incorporating trading volume in the equation for conditional variance of the generalized autoregressive conditional heteroscedasticity (GARCH) model on volatility persistence is investigated. Further, this study brings into play GARCH, GARCH-M, and EGARCH models conditioned to normal, student-t and generalized error distributions to model the dynamic structure of the NSE20 index for the period 2 January 2001 to 31 December 2017. The results disclose some well-known stylized facts of returns on stock, for instance, volatility clustering, heavy tails, leverage effects, and leptokurtic distribution. The estimates of parameters of the three models, that is, GARCH (1, 1), GARCH-M (1, 1), and EGARCH models report that the correlation between stock returns volatility and trading volume is positive and statistically significant. Moreover, estimates of the coefficients of EGARCH (1, 1) model report an increased measure of persistence on volatility as well as volatility asymmetry and the absence of leverage effect in the returned volatility. Also, the estimates of GARCH (1, 1) and GARCH-M (1, 1) parameters report that volatility persistence dwindles after trading volume is incorporated in the equation for the conditional variance.