Answer: 0.02801

## Explanation The DV01 (Dollar Value of a 01) measures the price sensitivity of a bond to a 1 basis point change in yield. ### Step 1: Calculate the price of the bond without embedded options Since the call option reduces the bond price, the price of a comparable bond with no embedded options is the sum of the callable bond price and the call option price: - At 3.95%: 97.9430 + 2.1972 = 100.1402 - At 4.00%: 97.8910 + 2.1090 = 100.0000 - At 4.05%: 97.8566 + 2.0035 = 99.8601 ### Step 2: Apply the DV01 formula $$ \text{DV01} = -\frac{\Delta P}{10,000 \cdot \Delta y} $$ Using the prices at 3.95% and 4.05% (10 bps change): $$ \text{DV01} = -\frac{99.8601 - 100.1402}{10,000 \cdot (0.0405 - 0.0395)} = -\frac{-0.2801}{10,000 \cdot 0.001} = \frac{0.2801}{10} = 0.02801 $$ ### Why other options are incorrect: - **B (0.01399)**: Uses only the price difference between 4.00% and 4.05% - **A (0.00864)**: Uses only the callable bond prices without considering the embedded option - **C (0.01402)**: Incorrect calculation using partial information

Author: LeetQuiz Editorial Team