Financial Risk Manager Part 2

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Explanation:

In the Cox-Ingersoll-Ross (CIR) model, the change in the short-term rate is calculated as: $dr = a(b - r)dt + \sigma \sqrt{r} dw$

Where: $a = 0.05$ $b = 0.075$ $r = 0.05$ $dt = 1/12$ $\sigma = 0.008$ $dw = 0.3$

$dr = 0.05 \times (0.075 - 0.05) \times (1/12) + 0.008 \times \sqrt{0.05} \times 0.3$ $dr = 0.000104 + 0.0005367 = 0.00064$

New rate $= r + dr = 0.05 + 0.00064 = 0.05064$ or $5.064%$, which matches closest to 5.06%.

Explanation:

In the Cox-Ingersoll-Ross (CIR) model, the change in the short-term rate is calculated as: $dr = a(b - r)dt + \sigma \sqrt{r} dw$

Where: $a = 0.05$ $b = 0.075$ $r = 0.05$ $dt = 1/12$ $\sigma = 0.008$ $dw = 0.3$

$dr = 0.05 \times (0.075 - 0.05) \times (1/12) + 0.008 \times \sqrt{0.05} \times 0.3$ $dr = 0.000104 + 0.0005367 = 0.00064$

New rate $= r + dr = 0.05 + 0.00064 = 0.05064$ or $5.064%$, which matches closest to 5.06%.

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Current short term rate	5%
Long run value of the short term rate	7.5%
Speed of mean revision adjustment	0.05
Volatility of rate change (σ)	0.8%
Random variable dw	0.3

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Last updated: July 5, 2026 at 07:20

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