Cox-Ingersoll-Ross Adjustment

In order to translate historical interest rate shocks into higher or lower interest rates regimes, we often apply what we refer to as a Cox-Ingersoll-Ross, or CIR, adjustment.

The basic idea is simple. If, in the past, an interest rate changed from 2% to 3%, we could say that the rate increased by 1% or 50%,

dR = 3% - 2% = 1%

dR/R = (3% - 2%)/2% = 50%

If the current interest rate is 10%, and we want to apply the same shock, we could argue that the interest rate should go to 11% or 15%,

10% + dR = 11%

10% + 10% x dR/R = 15%

There is a third option, though. The CIR interest rate model has a stochastic term that is proportional to the square root of the interest rate. We can do something similar in adjusting our historical shock

10% + dR x SQRT(10%/R) = 12.24%

Of the standard single-factor interest rate models, the CIR model is often the closest fit to historical data. For this reason, there is a good argument to be made for translating historical scenarios usnig the CIR adjustment.