1. You are an option dealer. Given a binomial model for stock prices, you sell call option where:
S0 Su Sd X r r
50 61 41 56 0.05 1/2
Number N of shares: 1000
a) Calculate the fair market price for the call option
b) Assume that you sell 1000 shares of the option for the fair market price + $0.12. How many shares of stock should you buy to hedge the sale?
c) What is your profit, independent of the outcome of stock price?
2. Assume that a stock model happens to have the parameters u=1.1, d=0.9, p=0.7, and we know that E(S2)= 27. Find S0 and all possible value for S1 and S2
3. A stock tree has three periods. The stock parameters are S0 = 21, u = 1.1, d = 0.8, and q = 0.7. Find E(S3)
4. Use the stock tree below, with a down and out barrier set $64, to find the option price at t=0 with X=$49 and r= 0.05