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Answer: -54,814
The estimated convexity is **B: -54,814**. Using the standard finite-difference convexity formula, \[ \text{Convexity} \approx \frac{P_{+} + P_{-} - 2P_0}{P_0 \, h^2} \] with \(P_{-}=102.07848\), \(P_0=101.61158\), \(P_{+}=100.92189\), and \(h=0.0002\), the result is approximately **-54,814** . ### Why it is negative A callable bond can have **negative convexity** because rising rates reduce the likelihood that the issuer will call the bond, while falling rates increase call risk and cap the price upside. That embedded call option makes the price-yield relationship bend inward, producing a negative convexity estimate .
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A risk manager is evaluating the price sensitivity of an investment-grade callable bond using the firm’s valuation system. The table below presents information on the bond as well as on the embedded option. The current interest rate environment is flat at 5%.
| Interest Rate Level | Callable Bond | Call Option |
|---|---|---|
| 4.98% | 102.07848 | 2.0871 |
| 5.00% | 101.61158 | 2.0501 |
| 5.02% | 100.92189 | 2.0131 |
The convexity of the callable bond can be estimated as:
A
-55,698
B
-54,814
C
-5,5698
D
-5.4814
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