A Statistical Analysis of Interest Rate Pricing

ABSTRACT

When small and medium-sized companies borrow from financial institutions and other sources, does the interest rate accurately reflect the credit risk? In order to explore this question, this report examines approximately 500,000 small and medium-sized companies in order to analyze changes in their interest rates and PD (Probability of Default) during the 9-year period between 1995-2003. The major findings are as follows:

First, the cross-section analyses for each year display almost the same distributions. Further, the results show that even if there is a deviation, there is still a chance of restoration. In this way, the distributions of both variables can be said to be constant.

Second, transitions of interest rates and PD from one year to the next are affected by their respective changes in the past (i.e. a history effect). Both variables also display a pullback tendency, where there is a high possibility that if they increase in one year, then they will decrease in the following year, or vice versa-in other words, that they will swing in the opposite direction from the previous year. Thus, changes in the interest rate and PD are decided by a tug-of-war between the force for the variables to converge into a stationary distribution and the force to make the variables stop at the original levels.

Third, when comparing changes in PD and interest rates, past changes have a weaker effect on interest rates than on PD. These findings imply that many financial institutions divide changes in PD into "trends of change" and "temporary change", and furthermore the potential for changes in interest rates may be limited to "trends of change" only.