Interest Rate Models

A quant is choosing between the Vasicek and Cox–Ingersoll–Ross (CIR) short-rate models to calibrate to a curve where the policy rate is currently near zero.

Part A

Write down the SDE for each model and identify the key structural difference.

Part B

Explain why this difference matters when rates are near zero. Which model can produce negative rates, and under what condition does CIR keep rates strictly positive?

Part C

Given Vasicek parameters $a=0.10$, $b=0.05$, $\sigma =0.01$, and current short rate $r_0=0.04$, compute the price of a 1-year zero-coupon bond and the 1-year yield it implies.