Question:
Today, there is a European call option written on Microsoft stock that expires in exactly 147 trading days. The option has an exercise price of $40. The current price of Microsoft stock is $42.00. US Treasury Bills that mature at the option's expiration date have a continuously compounded annualized return of 1.25% (i.e., the risk-free rate is .0125). You have predicted that the standard deviation of the return on Microsoft stock from now until expiration is 30% annually.
1. Using Black/Scholes, what is your estimate of the value for the call option described above.
2. You see that the market price of this call option is $3.00. Explain why there might be a difference in the value you calculated and the market price. How should you react to this difference between the market price and your estimated value? Might you legitimately be uncertain about what to do? If so, explain why?
3. Using put-call parity and the Black/Scholes value for the call, calculate the price of a put option written on Microsoft that has the same strike price and expiration date as the call option described above.
4. As it turns out, the market price of the put is $2.00. Given the market price of the call (i.e., $3.00) and the put ($2.00), how should you react? Is there a problem in these market prices that you can exploit? If yes, tell me exactly what your strategy is, being precise about how much to buy or sell of what securities.