In the Cox-Ingersoll-Ross (1985)model,interest rates are specified by the following stochastic process: $d r _ { t } = k \left( \theta - r _ { t } \right) d t + \sigma \sqrt { r _ { t } } d W _ { t }$ The process for interest rates is mean-reverting if A) $k 0$ B) $k 0$ D) $\theta

Question

In the Cox-Ingersoll-Ross (1985)model,interest rates are specified by the following stochastic process: $d r _ { t } = k \left( \theta - r _ { t } \right) d t + \sigma \sqrt { r _ { t } } d W _ { t }$ The process for interest rates is mean-reverting if A) $k > 0$ B) $k < 0$ C) $\theta > 0$ D) $\theta < r _ { t }$

Quizplus · Accepted Answer

The process is mean-reverting if $k > 0$, because in this case the interest rate will tend to revert to the mean level $\theta$.

In the Cox-Ingersoll-Ross (1985)model,interest Rates Are Specified by the Following drt=k(θ−rt)dt+σrtdWtd r _ { t } = k \left( \theta - r _ { t } \right) d t + \sigma \sqrt { r _ { t } } d W _ { t }drt​=k(θ−rt​)dt+σrt​​dWt​

In the Cox-Ingersoll-Ross (1985)model,interest Rates Are Specified by the Following $d r _ { t } = k \left( \theta - r _ { t } \right) d t + \sigma \sqrt { r _ { t } } d W _ { t }$