Answer-first summary for fast verification
Answer: +\$2.75
Use the two-term approximation: \[ \Delta P \approx -D\,P\,\Delta y + \frac{1}{2}C\,P\,(\Delta y)^2 \] From the previous questions: - \(P \approx 94.182\) - \(D \approx 2.88\) - \(C \approx 8.49\) - \(\Delta y = -0.01\) for a 100 bp drop So: \[ \Delta P \approx -2.88(94.182)(-0.01) + \frac{1}{2}(8.49)(94.182)(0.01)^2 \] \[ \Delta P \approx 2.711 + 0.040 \approx 2.75 \] So the estimated price increase is approximately **+$2.75**, which is **C**.
Author: Manit Arora
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Question 161.3. If the interest rate drops by 100 basis points, what is the estimated change in the bond’s price given by a two-term Taylor series expansion (i.e., duration and convexity)?
A
+`$2.51`
B
+`$2.71`
C
+`$2.75`
D
+`$2.88`
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