An option with maturity in nine-months on a non-dividend stock currently priced at 60 is to be valued. The option is a European put.

1. Calculate the price of a $5 in the money option at time zero using a one period Binomial model if = 15%, = 6%, and we assume d=1/u.

2. Construct the two-period binomial tree and calculate the price of the same option in a above using a two period Binomial model if = 15%, = 6%, and we assume d=1/u.

3. Calculate the delta at time zero.

4. Set up the replicating portfolio at time zero.

5. Roll forward the initial replicating portfolio to time 4.5 months assuming the initial movement is down.

6. Calculate the delta at time 4.5 months.

7. Adjust the replicating portfolio as appropriate at time 4.5 months.

8. Roll forward the replicating portfolio.

9. Calculate the value of the option assuming the option is no longer European but American.

10. Explain the concepts of a replicating portfolio and self-financing portfolio referring to your answers above.