Suppose you generate a 5-year binomial interest rate tree using the information about the term structure presented below (you can click on this an open an Excel file).

You compute the value of a 5-year annual-pay 6% coupon bond (par value is 100) that is callable in one year (and every year thereafter) at par. The current value (Time 0) of this callable bond is 102.639.

Question 1

Calculate the value (at Time 0) of the embedded call option.

Question 2

To compute the effective duration and convexity of this bond you vary the par rate curve down/up by 40 basis points and compute new prices of 103.314 and 101.677.

Calculate the effective duration of the callable bond

Calculate the effective convexity of the callable bond

In one or two sentences, explain what it means for the convexity to be negative.

Mat parratepot Forward Fo 3 4 5 3.000% 3.250% 3.500% 4.000% 4.500% 3.00% 3.2541% 3.51183% 4.04143% 4.58589% 3.00% 3.5088% 4.0293% 5.6465% 6.7923% Mat parratepot Forward Fo 3 4 5 3.000% 3.250% 3.500% 4.000% 4.500% 3.00% 3.2541% 3.51183% 4.04143% 4.58589% 3.00% 3.5088% 4.0293% 5.6465% 6.7923%