Cox Ingersoll Ross Model – Solved Example

LOS: Calculate the short-term rate change and describe the basis point volatility using the CIR and lognormal models.

Question:

The short rate is currently observed to be 4.00% and it’s annualized standard deviation has been estimated to be 80 bps. Tabulated below are two parameters for the Cox Ingersoll Ross (CIR) model:

ParameterValue
Strength of Reversion ($k$)0.70
Long-run Interest Rate ($\theta$)7.00%

Using the above information, estimate the following:

  • The $\sigma$ parameter for this CIR model,
  • The “basis point volatility” if the short rate increases to 6.00%.
A.0.008 and 98 bps
B.0.04 and 98 bps
C.0.04 and 80 bps
D.0.008 and 80 bps