Interest rate risk modeling using semi-heavy tail Distributions of normal variance-mean mixtures: 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, with no returns, 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. These assumptions have been considered inaccurate and misleading. This research uses mixture models exhibiting properties that appropriately capture the peakedness and skewness of interest rates as fundamental variables in pricing. The models of the Normal Variance-Mean Mixtures shows better performance than the normal distribution. The GARCH model is used under the assumption that 91-day Treasury Bills interest rates follow a Generalized Hyperbolic distribution while the Commercial Bank interest rates follows a Normal Inverse Gaussian distribution. 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.