Suppose you have just purchased one share of Twitter stock for S50. The stock is

Question

Suppose you have just purchased one share of Twitter stock for S50. The stock is not expected to pay a dividend during the time you plan to hold it. You have forecasted that in one year the stock price will either rise to $65 or fall to $40. Suppose further that you can either buy or sell a call option on Twitter stock with a strike price of $52.50. Assume that this is a European style contract that expires exactly in one year and that the risk -free interest rate is 8%. (a) Calculate the hedge ratio (H). [3 Points] (b) If you wish to create a riskless portfolio, how many call options should you write given that you own 1 share of stock? [2 Points] (c) Based on your answer from Part (b), fill in the following table showing that you have created a riskless portfolio. [5 Points] Stock Price = $65 Stock Price = $40 Value of 1 Share Value of Call Options Total Payoff (d) Calculate the price of the call option [10 Points]

Explanation / Answer

a.

Considering a riskless portfolio consisting of long position in delta (D) shares and short on 1 call option with strike 52.5.

If the stock price moves up to 65 the value of portfolio =65D-Max(0,65-52.5) =65D-12.5

If the stock moves down to 40 the value of portfolio = 40D

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