You just sold to a client a custom-made 31-year bond which pays a single coupon of

$1M 30 years from now and $2M at maturity. You would like to hedge this liability.

Assume that the term structure is currently

at at 5%.

(a) Your rst idea is to synthetically replicate the liability. Construct the hedging

portfolio consisting of the following bonds paying annual coupons:

Bond Coupon rate (%) Maturity

A 0 31 years

B 4 30 years

C 6 30 years

The par values of the three bonds are $100.