10.2. A coupon bond is a bond that makes payments while the bond is alive
as well as at its terminal date. Continuous coupons are like dividend
°ows. Most coupons, however, are paid discretely. Price a 10 year
bond using the CIR interest rate model that pays 0:05 (5%) times its
face value at the start of every year, starting one year after it is issued
(assume a face value of 1). Use the parameters · = 0:1, ® = 0:05 and
¾ = 0:08.
A callable bond is like an option in that it can be exercised early but
the seller has the right to determine whether it is exercised. Price the
above coupon bond with the extra feature that the seller can call the
bond once a year right after paying the coupon. Essentially this means
that the exercise value is 1:05. If the bond is worth more than this
alive, it is optimal to call the bond.
Write a Matlab program that prices the coupon bond both with and
without the callable feature. Note that finsolve could be used to solve
this problem but it is ine±cient (you should make sure you understand
why). You should, therefore, write your own code to solve this problem,
preferably in the form of a function that can be reused for other bond
pricing problems. Your code should be robust so that features such as
the bond's horizon and how often it is callable can be easily altered.
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