Answer: 719.167

The correct answer to the question regarding the convexity of the callable bond is D, 719.167. Convexity is a measure of the curvature or the rate at which the duration of a bond changes as interest rates change. It is calculated as the second derivative of the price-rate function divided by the price of the bond. The formula provided in the question is used to estimate convexity by considering the bond prices at two different interest rate environments, one higher and one lower than the current rate, and then calculating the change in these prices per change in rate. The formula given is: \[ \text{Convexity} = \frac{1}{P} \left( \frac{P_1 - P_0}{(Ar)^2} + \frac{P_0 - P_2}{(Ar)^2} \right) \] Where: - \( P \) is the current price of the bond. - \( P_1 \) and \( P_2 \) are the bond prices at the higher and lower interest rate environments, respectively. - \( Ar \) is the change in the rate in one step, which is given as 0.05%. The calculation provided in the question uses the bond prices at the different interest rates and the change in rate squared (since \( Ar \) is 0.05%, \( (Ar)^2 \) is \( 0.0005^2 \) or \( 0.00000025 \)). The incorrect options (A, B, and C) are results of misapplying the formula by using incorrect values for \( Ar \) or \( (Ar)^2 \). Option A uses 0.10% instead of \( 0.0005^2 \), option B uses 0.05% instead of \( 0.0005^2 \), and option C uses the square of 0.10% instead of \( 0.0005^2 \). The correct application of the formula, using the square of 0.05%, leads to the correct answer, which is option D, 719.167.

Author: LeetQuiz Editorial Team