Computational Methods in Economics and Finance

HW 10

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.

HW 10

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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