Consider a two-date binomial model. A company has both debt and equity in its capital structure. The value of the company is 100 at Date 0. At Date 1, it is equally like that the value of the company increases by 20% or decreases by 10%. The total promised amount to the debt holders is 100 at Date 1. The riskfree interest rate is 10%.

1. What are the possible payoffs to the equityholders at date 1? What kind of financial product has the same payoffs? Please describe the detailed characteristics of the financial product.

2. What are the possible payoffs to the bondholders at date 1? Are they riskfree? What kind of financial product/portfolio has the same payoffs? Please describe the detailed characteristics of the financial product/portfolio.

3. What is the value of the debt at Date 0? What is the value of the equity at Date 0?

4. Suppose the government announces that it guarantees the company?s payment to the debtholders. How much is the government guarantee worth?

5. Now we extend the model to a three-date setting. At both Date 1 and Date 2, it is equally likely that the value of the company increases by 20% or decreases by 10%, as depicted in the graph below. Suppose there is an American put option written on the entire firm with strike price 100. What is the value of this American put at Date 0?

\fA) Value of put option at any node (Prob*Pay off at higher node+Prob*payoff at lower node)/(1+rF) Action Value of put option at T=1 is weighted average of pay off divided by risk free rate T=0 T=1 Value of put option T=2 Pay off Value not called 128 -78 0 48 2 Pay off at t=1 0 0.91 Value of Am 0.41 2 0.91 80 50 30 15.55 called Value of put option 20 Total 15.55 18 32 32 As it is american put option it will be called at 30 giving value of Rs 20 at t=1 node Strike price Probability up and down return Up 50 50% 60% Return Down -40% Risk free rate=Probability *return up+Probability *return down Risk free rate 10.0% B) American call option Pay off T=2 50 80 30 128 48 18 78 0 0 Node Higher Lower Node Expected Value of call option at t=1 is maximum of Weighted average value of pay of at that particular node if it is called Value if called at T=1 30 0 35.45 0 C) Put call parity therom does not hold for American put or call option as there is flexibility provided to option holder where they can call it any time before expiration just like shown in above calulation. Total Value of call option at t=0 16.12 0 16.12 9.09 9.50 merican put option at T=0