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You are expecting IBM stock price to go up in next 8 months, however you are not completely sure. So you decide to use just one option, either European call or European put on IBM stock maturing in 8 months to bet on your view about IBM’s stock price prospects. Suppose that the current stock price and the strike price for both call and put on the IBM stock is $50.
(a) What option will you invest in? Explain.  Call. Call price will go up if the stock price goes up. The losses are limited by the option premium paid.
(b) At what price will you breakeven if both put and call options are sold for the same premium of $5 Breakeven stock price $50+$5 = $55
(c) Assume that the risk free rate is 3% per annum. Also assume that the standard deviation of IBM’s stock return is 30% per year. What is the Black-Scholes value of the option you have identified in part a?
Step 1: find d1 and d2 d_1=(ln⁡(50/50)+(0.03+〖0.30〗^2/2)×8/12)/(0.30×√(8/12))=0.2041 d_2=0.2041-0.30×√(8/12)=-0.0408
Step 2: find N(d1) and N(d2) Using the cumulative normal table obtain N(d1) = N(0.20) = 0.5793 and N(d2) = N(-0.04) = 0.4841
Step 3: calculate the call option value c=$50×0.5793-$50×e^(-0.03×(8/12) )×0.4841=$5.2393
(d) What is the time value of the option you have identified in part a? Because the stock price equals the strike price ($50) the total value of the option would consist of time value only, therefore the time value of this option is $5.2393
Problem 2
You anticipate that the volatility of IBM stock will increase substantially over the course of next year, but you do not have a strong view about future direction of IBM stock price. Today you decide to enter a position in two at the money European IBM options maturing in one year. Today’s IBM stock price is $30 a share. The call option premium is $2 and the put option premium is $3.
(a) What options will you invest in?

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