From model 2 (drift and risk premium model), we have that:
$dr = \lambda dt + \sigma dw$

We are given that: $\lambda = 0.348\%,\ r_0 = 6.047\%,\ \sigma = 2.07\%$ and $dw = 0.32$

and that the time interval under consideration is one month or $\frac{1}{12}$ years.

Hence:
$dr = 0.348\% \times \frac{1}{12} + 2.07\% \times 0.32$
$\Rightarrow dr = 0.6914\%$

Things to Remember

• Drift and risk premium model is used to calculate the change in interest rates based on a constant term, volatility, and a random variable.
• The drift term represents the expected change in interest rates over time, while the risk premium term captures the impact of random fluctuations.
• Volatility is a measure of the variability of interest rates and is an important input in models that involve random movements.
• Random variables like dw represent the uncertainty or randomness in the interest rate movements.
• When calculating changes in interest rates, it's important to consider the time interval over which the change is occurring.