Question

2. Options, risk, and the option premium. The current market price of a large corporation’s stock is $255. You purchase the stock for this price. After one month, there is a 80% chance that price will rise to $260 and a 20% chance it will fall to $240.

a. What is the expected return and standard deviation of the returns on buying one share of this stock (returns = selling price – purchase price)?

b. Suppose you held a one-month call option on the stock with a strike price of $250. If we only take into account the changes in the stock price (ignore the price of the option), what is the expected value and standard deviation of the returns on this option? Compare to your answer in ‘a’.

c. What is the intrinsic value (per share) of the option described in ‘b’? If the option is selling for $12/share, what is the time value per share?

d. Now assume that the price of the same stock will rise to $280 with a 80% probability or fall to $180 with a 20% probability. Also, suppose you had the same one-month option with a strike price of $250. If we only take into account the returns associated with the option (ignore the price of the option) what is the expected value of the returns on this option? Would you pay more or less for this option compared to what you would pay given the situation in ‘b’?

Answer 1