On Measuring Skewness and Kurtosis in Short Rate Distributions: The Case of the U.S. Dollar London Inter Bank Offer Rates

February 25, 2001

It has been observed that return distributions in general and interest rates in particular exhibit skewness and kurtosis that are inadequately modeled by the lognormal distribution.

We have modeled the skewness and kurtosis of the short rate using the g-and-h distribution and Generalized Beta Distribution of the Second Kind (GB2) and compare their performance. The g-and-h distribution is a functional transformation of the standard normal distribution and spans a much wider area in the skewness-kurtosis plane than many well-known skewed and leptokurtic distributions including GB2. Researchers have used these distributions in modelling many different asset price and return distributions. However, none of these works have dealt with interest rates of any kind, nor did they compare the fit of their proposed distributions to those of others.
GB2 and g-and-h are both four-parameter distributions and many well-known distri-butions can be derived as special cases of parameter values from each of these distributions. We observed that the g-and-h distribution exhibited a very high degree of accuracy in modelling the U.S. Dollar 1- and 3-month historical LIBOR rates, and much more than exhibited by GB2.

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