Financial Risk Manager Part 2

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Explanation:

Under Model 2,

dr = \lambda dt + \sigma dw

where:

$dr =$ change in interest rates over small time interval, $dt$

$\lambda =$ drift

$dt =$ small time interval (measured in years) (e.g., one month = $1/12 $, 2 months = `$ 2`/12$, and so forth)

$\sigma =$ annual basis-point volatility of rate changes

$dw =$ normally distributed random variable with mean 0 and standard deviation $\sqrt{dt}$

Thus, the change in the short-term rate is given by:

\begin{aligned} dr &= \lambda dt + \sigma dw \\ &= 0.25\% \times \frac{1}{12} + 1.15\% \times 0.25 \\ &= 0.3083\% \end{aligned}

Since the short-term rate started at 5.26%, the short-term rate after a month is 5.5683%:

\text{New short-term rate} = 5.26\% + 0.3083\% = 5.5683\%

Explanation:

Under Model 2,

dr = \lambda dt + \sigma dw

where:

$dr =$ change in interest rates over small time interval, $dt$

$\lambda =$ drift

$dt =$ small time interval (measured in years) (e.g., one month = $1/12 $, 2 months = `$ 2`/12$, and so forth)

$\sigma =$ annual basis-point volatility of rate changes

$dw =$ normally distributed random variable with mean 0 and standard deviation $\sqrt{dt}$

Thus, the change in the short-term rate is given by:

\begin{aligned} dr &= \lambda dt + \sigma dw \\ &= 0.25\% \times \frac{1}{12} + 1.15\% \times 0.25 \\ &= 0.3083\% \end{aligned}

Since the short-term rate started at 5.26%, the short-term rate after a month is 5.5683%:

\text{New short-term rate} = 5.26\% + 0.3083\% = 5.5683\%

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Last updated: July 5, 2026 at 07:18

5.5%

5.5683%

4.5212%

0.3083%