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Answer: 719.2
D is correct. Effective convexity measures the sensitivity of the duration measure to changes in interest rates. It is given by the formula: \( \frac{1}{P} \left( \frac{P_{+} - P_{-}}{2P} \right)^2 \) where \( P_{+} \) is the value of the bond when all rates increase by \( \Delta r \) and \( P_{-} \) is the value of the bond when all rates decrease by \( \Delta r \). Therefore, the best estimate of convexity is: \( \frac{97.8566 + 97.9430^2}{2 \times 97.8910} \times \frac{1}{0.00052} \approx 719.1672 \)
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A risk manager is evaluating the price sensitivity of an investment-grade callable bond. The data collected on the bond and its embedded call option are shown in the table below:
| Interest Rate Level | Callable Bond Price | Call Option Price |
|---|---|---|
| 3.95% | 97.9430 | 2.1972 |
| 4.00% | 97.8910 | 2.1090 |
| 4.05% | 97.8566 | 2.0035 |
Assuming that the current interest rate curve is flat at 4%, calculate the approximate effective convexity of the callable bond.
A
18.0
B
36.0
C
179.0
D
719.2
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