In the Cox-Ingersoll-Ross (CIR 1985) model, you are given that $d r _ { t } = \kappa \left( \theta - r _ { t } \right) d t + \sigma \sqrt { r _ { t } } d W _ { t }$ where $x = 0.5$ , $\theta = 0.06$ , $\sigma = 0.10$ , and the current short rate of interest is $r _ { 0 } = 0.08$ . What is the expected short rate of interest one year hence?
A) 6.6%
B) 7.2%
C) 7.6%
D) 8.2%

Question

Quizplus · Accepted Answer

The expected short rate of interest one year hence can be calculated using the formula for the expected value of $r_t$ in the Cox-Ingersoll-Ross model: $E[r_t] = r_0 e^{-\kappa t} + \theta(1 - e^{-\kappa t})$. Substituting the given values ($\kappa = 0.5$, $\theta = 0.06$, $r_0 = 0.08$, and $t = 1$), we get $E[r_1] = 0.08e^{-0.5} + 0.06(1 - e^{-0.5}) \approx 0.072$ or 7.2%.

In the Cox-Ingersoll-Ross (CIR 1985) Model, You Are Given That drt=κ(θ−rt)dt+σrtdWtd r _ { t } = \kappa \left( \theta - r _ { t } \right) d t + \sigma \sqrt { r _ { t } } d W _ { t }drt​=κ(θ−rt​)dt+σrt​​dWt​

In the Cox-Ingersoll-Ross (CIR 1985) Model, You Are Given That $d r _ { t } = \kappa \left( \theta - r _ { t } \right) d t + \sigma \sqrt { r _ { t } } d W _ { t }$