Question

Consider a bond P with 15 year maturity, 6% coupon annually paid, yield to maturity 7%.

The dollar convexity is

Answer 1

The dollar convexity is 120.44.

Explanation:

Dollar convexity measures the dollar value of the curvature of the price/yield curve.

Assume the following from the question,

Step 1: We have to presume that the Bond Par value is 1000

Step 2: The bond has 15 coupon payments remaining, i.e none of coupon payment have elapsed.

$\text{ Dollar Convexity }= \text{ Convexity}\times\text{ Initial Bond Price }}$

Convexity=$\frac{1}{(1+YTM^2)} \times\frac{\text{total Cash flow at time 15 years}}{(1+YTM)^{15}}\times 15^2+15$

Initial Bond Price is calculated as follows,

Bond Price= $\frac{60}{1+0.07} + \frac{60}{(1+0.07)^2}+ \frac{60}{(1+0.07)^3}$ .....for 14 years $+ \frac{1060}{(1+0.07)^{15}}= 908.92$

On substituting the value we get = $7.55\times908.92$ (Initial Bond Price)= 120.44

So, Dollar Convexity = $7.55\times908.92= 120.44$

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