Financial Risk Manager Part 1
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A log trend model is approximated on the interest rate (in %) movement in a certain market based on data from 2000 until 2020. The estimated model is given as:
The standard deviation of the residual is 0.0342. Assuming that the residuals are normally distributed, what is the 95% confidence interval for interest rate movement for year 2023?
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TTanishq
A
[12.030, 13.754]
B
[12.018, 13.739]
C
[-0.0584, 0.0756]
D
[11.994, 13.713]
Explanation:
Explanation
For a log-linear model with normally distributed residuals, the 95% confidence interval for the forecast is calculated using:
- Expected value of ln(Y_T):
\mathrm{E}_T[\ln Y_T] = -0.1567 + 0.00134 \times 2023 = 2.554$`$2`. **Variance adjustment**:
\frac{\sigma^2}{2} = \frac{0.0342^2}{2} = 0.00063
. **Expected value of Y_T**: $$\mathrm{E}[Y_{2023}] = \exp(2.554 + 0.0006) = 12.866$4`. **Error bounds multiplier**: $$\exp(\pm 1.96 \times 0.0342) = [0.935, 1.069]$5. 95% Confidence Interval: 95`%\text{CI}_{2023} = [0.935 \times 12.866, 1.069 \times 12.866] = [12.030, 13.754]$$
This approach accounts for the log-normal distribution properties and provides the correct confidence interval for the interest rate forecast.
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