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Answer: -0.40% | 4.60%
## Explanation In Model 1 (Vasicek model), the change in the spot rate is given by: $$dr = \sigma \cdot dW$$ Where: - $\sigma$ = annual volatility = 80 bps = 0.80% - $dW$ = -0.5 **Step 1: Calculate the change in spot rate** $$dr = \sigma \cdot dW = 0.80\% \times (-0.5) = -0.40\%$$ **Step 2: Calculate the new spot rate** Current rate = 5.00% New rate = Current rate + Change in rate = 5.00% + (-0.40%) = 4.60% **Key Points:** - Model 1 assumes no drift term, so the expected change is zero - The actual change depends on the realization of the random variable dW - With dW = -0.5, we get a negative change in the interest rate - The annual volatility is applied directly to the random shock Therefore, the correct answer is **B: -0.40% | 4.60%**.
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Using Model 1, assume the current short-term interest rate is 5%, annual volatility is 80bps, and dW, a normally distributed random variable with mean 0 and standard deviation √dt, has an expected value of zero. After one month, the realization of dW is -0.5. What is the change in the spot rate and the new spot rate?
A
0.40% | 5.40%
B
-0.40% | 4.60%
C
0.80% | 5.80%
D
-0.80% | 4.20%
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