Question

A bond has 3 years to maturity, a 10% annual coupon and a par value of $100. The bond
pays a continuously compounded interest of 7%. Suppose the interest rate goes down to 6%. What
would be the percentage change in the price of the bond implied by the duration plus convexity
approximation?

Answer 1

As a first step we need to calculate the price, duration, modified duraton and convexity of the bond. Before doing so, we need to convert the continuously compounded interest rate to annual compounded interest rate using er = 1 + R

Hence R = er - 1 = e0.07 - 1 = 7.2508%

Now the continuously compounded interest rate changes to 6%, hence, the equivalent annual compunde rate = e6% - 1 = 6.1837%

Hence, change in annual yield = Δy = 6.1837% - 7.2508% = -1.0672% = -0.010672

Hence, the percentage change in the price of the bond implied by the duration plus convexity
approximation = - modified duration x Δy + 1/2 x convexit x (Δy)2 = -2.55933 x (-0.010672) + 1/2 x 9.25294 x (-0.010672)2 = 0.0278 = 2.78%