Interest Rate Risk Modelling Using Semi-Heavy Tail Distributions of Normal Variance-Mean Mixtures: A Study on Central Bank of Kenya Interest Rates

Abstract

Derivative prices such as options and bond prices as well as swaps depend on the distributional assumptions of the underlying economic variables, normally, interest rates. The risk associated with changes in interest rates may worsen the value of the contract that depend on it since the values of these assets (derivative contracts) are affected directly by the fluctuations in interest rates. The distribution of interest rates, therefore, needs to be well understood to reduce the risks of losses associated with it. The Binomial Option pricing model assumes that interest rates are constant throughout the life of the option. Another common assumption of the underlying economic variables is that their returns are normally distributed with constant volatility. These assumptions have been used in pricing derivatives and currencies and has led to over-pricing and in some cases under-pricing. The models of the Normal Variance-Mean Mixtures used in this research shows better performance than the normal distribution. Weekly 91-day and commercial bank interest rates are used from 1991 to 2021. This study will provide a better model for interest rates to avoid mispricing. We find that the 91-day Treasury Bills interest rates follow a Generalized Hyperbolic distribution while the Commercial Bank interest rates follows a Normal Inverse Gaussian distribution. G.A.R.C.H model is then used in forecasting under each of the above findings. A 99pc Value at Risk is then computed for the two models and calculates the minimum expected returns in the subsequent months. This research forms a foundation for the development of advanced pricing models that incorporates the fluctuations of interest rate in the pricing industry. We conclude that the Normal Inverse Gaussian and Generalized hyperbolic distributions provide better fits than the assumed normal distribution.