The term structure of interest rates is flat at 4.3 %, but rates could change immediately to 6.3 % or 2.3 % with probability of 0.48 and 0.52 , respectively, and stay at that level forever. You purchase a putable bond with 30 years to maturity, 4.3 % coupon paid annually and par value of $100. The putable bond can be put at $ 98 immediately.

a. At what interest rate will the bond be put?

b. what is the price of this putable bond? (in 2 decimal places)

c. what is the expected price of a straight bond with same characteristics of this putable bond? (in 2 decimal places)

d. what is the price of the embedded put option? (in 2 decimal places)

e. what is the yield spread of the putable bond over the straight bond with same characteristics? (should be %, beware of +/- signs)