You are given the following information on a European Call Option. The option matures in 10 weeks and is at the money. The current stock price of the underlying stock is $75.00. Assume that the stock price can either go up by 20% or go down by 10% each period. The risk free rate is 5.0% per year. Compute the following using a 2-period Binomial Model (so, each period is 5 weeks): Set up a replicating portfolio of the stock and a risk free bond. i. Clearly show the payoff for the Stock, Bond and the Call in both periods. ii. Calculate the Number of Stocks and Bonds in both periods required to replicate the call. Using no Arbitrage, compute the price of the Call option (CBin) using this replicating portfolio. Compute the probability (implied) that the Option will be exercised. Compute the annualized standard deviation (sigma (B-S-M) of the stocks return (Sigma for B-S-M). Compute the Black-Scholes-Merton theoretical option price for the Call option (CBSM). Compute the price of a B-S-M Put option using Put-Call Parity

4. Use relevant information (S0, K, Rf, T, Sigma) from the above question to construct a delta- hedging table for 100 short call options as in the lecture slides (the class lecture used 100,000 short calls). To do this, execute the following steps. a. Construct two tables for the end of each week for the next 10-weeks. Thus, you are delta- hedging once every week, i.e. for weeks 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (when option matures); i. Table 1 is when the option matures in-the-money. ii. Table 2 is when the option matures out-of-the-money. b. For both tables, show that the annualized standard deviation or stock returns from the 10 weeks is approximately equal to the annualized standard deviation in 4d, above. c. Clearly show the payoffs, profits, and all relevant cash flows at the end of the term (10 weeks). d. Compare the price of the call option in Question 3e with the present value of the average price per call option in this question (using 4c). and explain in 2-3 sentences what you find.