This question has multiple, parts I solved the first one.

In this question, we ask you to revisit option pricing and calibrating binomial models. To begin with, assume the term structure implied by bond prices is the same as the extended example in the lecture notes. That is, Recalculate the three-period binomial tree with risk-neutral probability. In calculation, assume the annual volatility is 14% and follow the procedure of bootstrapping along the tree. (It is easiest to do this using the tree-fitter spreadsheet, available with the class materials.) Hint: Use e21 as the volatility parameter if using the provided tree-fitter spreadsheet. (a) What is the binomial tree for one-year rates? Write your answers in unit of percentage points. \begin{tabular}{|c|c|c|} \hlinet=0 & t=1 & t=2 \\ \hline \multirow{8}{*}{r0=3.5000%} & & rHH=7.5404% \\ \hline & & \\ \hline & rH=5.2533% & \\ \hline & & \\ \hline & & rHL=5.4583% \\ \hline & & \\ \hline & rL=3.8027% & \\ \hline & & rLL=3.9512% \\ \hline \end{tabular} (b1) What is the price of a three-year 5.25% bond (face value of $100 ) with an American call option, callable ex coupon at times 1 and 2 at $99.50 ? (b2) What is the yield spread between the callable and non-callable bonds? Use yield to maturity (annual basis) with simple compounding and write your answer in unit of percentage points. (c1) Now assume that the bond in part (b) has an attached American put option as well as the American call option. In particular, the bond can be put to the issuer at a price of $99 at the end of times 1 or 2 . For this bond at each node in times 1 and 2 , what is the optional strategy, and what is the associated value of the position ? HH $ HL $ $ H $ L $ (c2) What is the price of the bond described above and what is the price of the associated American put option? Bond with both call and put $ Associated American put option $