1. You are given the following information on a European Call Option. The option matures in 0.5 years and is at the money. The current stock price of the underlying stock is $90.00. 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:

1. Set up a replicating portfolio of the stock and a risk free bond and use a two-period binomial model.
   1. Clearly show the payoff for the Stock, Bond and the Call in both periods.
   2. Calculate the Number of Stocks and Bonds in both periods required to replicate the call.
2. Using no Arbitrage, compute the price of the Call option (C_Bin) using this replicating portfolio.
3. Compute the probability (implied) that the Option will be exercised.
4. Compute the annualized variance of the stocks return (Sigma for B-S-M).
5. Compute the Black-Scholes-Merton theoretical option price for the Call option (C_BSM).
6. Compute the price of a Put option.