Almost all option pricing models are based on the concept of a riskless hedge. I

Question

Almost all option pricing models are based on the concept of a riskless hedge. Investors can create a riskless hedge by purchasing shares of stock and simultaneously selling a call option on the stock. Suppose Randall and Arts Inc. stock is currently selling for $70.00 per share. Options exist that permit the holder to buy one share at an exercise price of $65.00. These options will expire at the end of one year. When the options expire, Randall and Arts Inc.'s stock will either be selling for $85.00 or $45.00. What is the range of Randall and Arts Inc.'s ending stock prices? $50.00 $45.00 $40.00 $25.00 What is the range of Randall and Arts Inc.'s ending option values? $20.00 $25.00 $15.00 $35.00 To construct a riskless portfolio, an investor will need to equalize these ranges. If the investor is planning on selling one option, how many shares of stock should he or she buy to equalize these ranges? Assume that for this problem you can buy less than one share of stock. 0.65 0.50 0.40 0.70 If the investor decides to go forward with creating this riskless hedge, what will the ending total value of the portfolio be? $22.50 $21.25 $18.75 $20.75 What will the equilibrium price of the call option be if the risk-free rate is 7%? $12.57 $13.27 $13.97 $11.18

Explanation / Answer

The range of ending stock prices = Highest price – Lowest price

                                                     = $85 - $45

                                                     = $40

Answer: third option

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