5. Interest Rate Models

Short Rate Models — Quiz

Test your understanding of short rate models with 5 practice questions.

Practice Questions

Question 1

For the Vasicek model, the function B(t,T) in the bond pricing formula $P(t,T)=A(t,T)e^{-B(t,T)r_t}$ is given by $B(t,T)=\frac{1-e^{-\alpha (T-t)}}{\alpha}$. If $\alpha=0.2$, $t=0$, and $T=5$, what is $B(0,5)$ approximately?

Question 2

In the Vasicek zero-coupon bond pricing formula $P(t,T)=A(t,T)e^{-B(t,T)r_t}$, what is the primary role of the function $A(t,T)$?

Question 3

In the Vasicek short-rate model $dr_t=\alpha(\beta - r_t)dt+\sigma dW_t$, increasing $\alpha$ (holding $\beta$ constant) will have which effect on the short-rate behavior?

Question 4

For the CIR model $dr_t=\alpha(\beta - r_t)dt+\sigma\sqrt{r_t}\,dW_t$, the Feller condition is $2\alpha\beta\ge\sigma^2$. What does satisfying this condition guarantee?

Question 5

Which property of the Vasicek model allows derivation of a closed-form analytic formula for zero-coupon bond prices?