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Q1. The stock index is currently 1500. The risk free rate is 4% per year. Calculate the value of the call option and the other values (given below) using a two period (two step or state) binomial tree. Assume that the strike price of the index is 1480 and the stock can go up by 15% and fall by 5%.

a) Find the two stage movement of the stock price if the stock can go up by 15% and fall by 5%?

b) Find the option values for the second period in a two stage (or state) binomial tree?

c) Find the risk neutral probability and hedge ratios?

d) Find the value of a call for a two period binomial tree at time period 0 and time period 1?

e) Find the value of call option and the stock portfolio at every stage of the hedge? Effectively show that how dynamic hedging model works using two period binomial tree? Prove that if a portfolio of stocks and options is fully hedged we will only earn risk-free rate?

Q2. Suppose an American put is trading for $15 and an American Call is trading tot $13.50, where both options have identical trading terms. The underlying stock puce is 4$953 and exercise price is $99. The annual risk-free rate is 5 percent and time to expiration cot  both options is one year. Assuming that the stock pays no dividend, Identify if you can  develop an arbitrage strategy. If there is an arbitrage using put-call parity, how will you generate arbitrage profits? Show the exact amount..

Q3. The following option prices were observed for a stock for July 6 of a particular year. Use this information to answer the following questions. The stock is currently priced at $155. The expiration of the option is on July 17'h.

Strike    Calls       Puts
155       $3.00     $2.50
160       $0.60     $5.90

Use the following possible prices and determine the profit for these possible stock prices of $145, 150, 155, 160, 165, 170.

a) Buy one July 17, 160 call contract. Hold it until the option expires. Determine the profits and graph the results. Find the beak-even point for both 155 and 160 call.

b) Buy one July 17, 155 put contract. Determine the profits and graph the results. Find the beak-even point for both 155 and 160 put option.

c) Sell one July 17, 160 put contract. Hold it until the option expires. Determine the profits and graph the results. Calculate both maximum profit and loss?