
Explanation:
B is correct. The forecast confidence interval depends on the variance of the forecast error. When the error is Gaussian white noise , then the constructed confidence interval for the future value follows a normal distribution. The 95% confidence interval for the forecast of the option contract price is given by:
Note that the time expectation or forecast of is given by:
Therefore,
The 95% confidence interval is then: 343.6 ± 1.96(4.62) = 343.6 ± 9.0552, which gives [EUR 334.54, EUR 352.65].
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Q-66. An analyst at a hedge fund is constructing a 95% confidence interval for the 2-month point forecast of the price of a standard option contract on 100 shares of a stock, measured in EUR, using the linear time trend model utilized by the fund. The analyst refers to the model estimated using monthly option prices (OP) over the last 5 years, which is denoted by the following equation:
where (current month) is equal to 0, is the horizon of the forecast, and is Gaussian white noise. The estimate of the residual standard deviation, , is 4.62. What is the correct 95% confidence interval for the price of the option contract?
A
[EUR 322.04, EUR 340.15]
B
[EUR 334.54, EUR 352.65]
C
[EUR 336.02, EUR 351.18]
D
[EUR 338.98, EUR 348.22]
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