Explanation

Convexity is defined as the second derivative of the price-rate function divided by the price of the bond. To estimate convexity, one must first estimate the difference in bond price per difference in the rate for two separate rate environments, one a step higher than the current rate and one a step lower. One must then estimate the change across these two values per difference in rate. This is given by the formula:

$$C = \frac{1}{P_0} * \frac{\frac{P_1 - P_0}{\Delta r} - \frac{P_0 - P_{-1}}{\Delta r}}{\Delta r} = \frac{1}{P_0} * \frac{P_1 - 2P_0 + P_{-1}}{(\Delta r)^2}$$

where $\Delta r$ is the change in the rate in one step; in this case, 0.05%. Therefore, the best estimate of convexity is:

$$C = \frac{1}{97.8910} * \left[ \frac{97.8566 - 2*97.8910 + 97.9430}{(0.0005)^2} \right] = 719.1672$$

Why other options are incorrect:

• A (0.180): This result is obtained when the change in yield in the formula is taken as 0.10% instead of the square of 0.05%.
• B (0.360): This result is obtained when the change in yield in the formula is taken as 0.05% instead of the square of 0.05%.
• C (179.792): This result is obtained when the change in yield in the formula is taken as the square of 0.10% instead of the square of 0.05%.