# Calculation of Forward Price of a Stock that Pays no Dividend

Question

Consider a stock that pays no dividend trading at \$100.  Suppose one-year call options with strike prices of \$95, \$100, \$105, and \$110 can be bought for a premiums of \$16.41, \$12, \$9, and \$7.24 respectively.  Suppose the annual effective interest rate is 5% (i.e., a \$100 bond pays \$105 one year from now).

• What are the values of one-year puts with strike prices corresponding to those listed for the call options above?
• Suppose you wished to enter into a long one-year forward position on the stock.  What is the fair forward price?
• Suppose a dealer offers to take the other side of your forward at a price of \$104 (i.e., she agrees to sell the stock to you for \$104 in one year). Is this a fair priced offer according to arbitrage pricing theory (assume that you can borrow and lend at an annual effective interest rate of 5%; and that you can buy and short the stock without transaction costs)?  If not, what payment now (either from you to the dealer, or from the dealer to you) would make it fair?  Specify in your answer the amount and who makes the payment and who receives it.
• Suppose that you cannot find a counter party for your desired long forward position. Using only the calls and puts described above, how would you synthesize a long (on market) forward position?
• Suppose that you wished to hedge your long position in such a way that your payoff would never be below \$95. How could you accomplish this using the options (both the calls, and the puts) described above without incurring any net out of pocket cost?  Assume there are no transactions costs.

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