Use the minimum constraint approach.

d. Using the binomial interest rate tree, show at each node the call option values of the callable bond (CP = 99). Given your call option values, determine the values at each node of the callable bond as the difference between the option-free values found in Question 1.b and the call option values. Do your callable bond values match the ones you found in Question 1.c?

e. Comment on values of your call options being equal to the present value of the interest savings the issuer realizes from refunding the bond at lower rates.

f. Using the binomial interest rate tree, determine the value of the bond assuming it is putable in periods one and two at a put price of PP =