In the Cox-Ingersoll-Ross (1985) model, interest rates are specified by the following stochastic process: $d r _ { t } = k \left( \theta - r _ { t } \right) d t + \sigma _ { } \sqrt { r _ { t } } d W _ { t }$ Implementation of the model to match observed nominal rate processes generally requires of the parameters that
A) $k 0$
B) $\theta 0$
C) Both (a) and (b).
D) Neither (a) nor (b).

Question

In the Cox-Ingersoll-Ross (1985) model, interest rates are specified by the following stochastic process: $d r _ { t } = k \left( \theta - r _ { t } \right) d t + \sigma _ {  } \sqrt { r _ { t } } d W _ { t }$ Implementation of the model to match observed nominal rate processes generally requires of the parameters that
A) $k > 0$
B) $\theta > 0$
C) Both (a) and (b).
D) Neither (a) nor (b).

Quizplus · Accepted Answer

The Cox-Ingersoll-Ross (CIR) model requires $k > 0$ to ensure mean reversion towards the long-term mean interest rate $\theta$, and $\theta > 0$ to ensure positive interest rates, thus both (a) and (b) are required.

In the Cox-Ingersoll-Ross (1985) Model, Interest Rates Are Specified by the Following