1. Consider the following stock price tree in which each time period is one day:

The initial stock price is $85. Assume that the annual interest rate is r = 5% and that interest is being compounded continuously.

(a) Find a fair price of an European put option with strike price X = $90 on this stock.

(b) Suppose that you are a dealer and that you sell one European put option at the fair market price. Illustrate the idea of hedging on the paths ud and dd.

(c) Find a fair price of an European call option with strike price X = $85 on this stock.

(d) Suppose that you are a dealer and that you sell one European call option at the fair market price. Illustrate the idea of hedging on the paths uu and du.