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During the upcoming year, the stock price of Delinquent Joe Inc. (DJ) is expected to go up to $290 or down to$170 with equal probabilities. The beta of the stock is equal to 0.75. The annual risk free rate is 10.5% and the expected annual return on the market is 16.5%. You are interested in replicating and pricing a European call option on DJ's stock. The option has a strike price of $212 and will mature in one year.
a. What is the current price of DJ's stock?
b. Using the stock and borrowing/lending at the risk free rate, form a portfolio that will replicate the call option. How many shares of DJ will you buy/sell, and how much money will you borrow/lend?
c. Use the portfolio derived above to price the call option.
d. What is the beta and expected return of the call option?
e. Using the result from part(d) show that the price of the call option found in part c) can also be derived by discounting the expected cash flow of the option.
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