MSc.MF Theses and Dissertations

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Browsing MSc.MF Theses and Dissertations by Subject "Calibration"

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    Calibration of vasicek model in a hidden markov context: the case of Kenya
    (Strathmore University, 2017) Chelimo, John Kigen
    This dissertation calibrates the Vasicek term-structure model to the evolution of interest rate dynamics in Kenya. This is done for both a single-state and a multi-state model using state estimated under a Hidden Markov Model (HMM). The findings of this paper provide a starting point for the management of the risk posed by interest rate-dependent instruments.The Vasicek model is calibrated using monthly observations of the 91-day treasury bill rate from September 1994 to July 2014 as a proxy for the short rate. Key results show an increase in the mean reversion parameter with an increase in the number of states, suggesting higher stability of states. The volatility is observed to move independently of the level of the interest rate,supporting the idea that risk is not necessarily a function of the level of the interest rate but rather related to the inherent variability of rates in a particular state. Findings from this parameter estimation provide support for interest rate models that incorporate regime switches.
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    A Comparative study on mathematical models for interest rate dynamics: a Kenyan case study
    (Strathmore University, 2021) Maina, Hudson Mwangi
    This dissertation calibrates equilibrium one-factor short-term interest rate models to the evolution of interest rate dynamics in Kenya. The aim of the study is to find out which one-factor short-rate model best captures the dynamics of the short-term interest rate in Kenya. Additionally, the study aims to evaluate the relationship between conditional volatility of interest rate changes and the level of interest rate. The findings of this study provide a basis for valuation of contingent claims and hedging of interest rate risk. The data used in the study was obtained from the Central Bank of Kenya (CBK) website 1 for the period between January 2005 to July 2016. Since the short-term interest rate is unobservable in the market the 91-day Treasury Bill (TB) rate was used as its proxy. The Generalized Method of Moments (GMM) estimation technique was used to obtain the parameters for all the models under study. Key results showed that there is weak evidence of mean reversion for all the models evaluated. Furthermore, it was established that there exists a positive relationship between interest rate volatility and the level of interest rate. The best performing model from the study is determined to be the Chan, Karolyi, Longstaff and Sanders (CKLS) model which allows the volatility of interest rate changes to be highly dependent on the level of the interest rate. This model also has the best volatility forecasting ability among the models under study. It is therefore recommended to interest rate policy makers for use in their work.