1. You want to speculate on an increase in the price of a certain stock. The current stock price is $29. A 3-month call with a strike price of $30 costs $2.90. You have $5,800 to invest. Identify two alternative strategies, one in the stock and the other in an option on the stock. What are the potential gains and losses from each? (Hint: Create a table showing the gains/losses for each strategy at different prices and draw the diagrams, superimposed on each other).
2. Binomial tree. A stock price is currently $40. It is known that at the end of 1 month it will be either $42 or $38. The risk-free rate is 8% per annum with daily compounding. What is the value of a 1-month European put option with a strike price of $39? [Hint: Use exactly the same procedure as the call option but evaluate the put option payoffs instead].
3. Black-Scholes Model. What is the price of a European call option on a stock when the stock price is $52, the strike price is $50, the risk-free rate is 12% per annum, the volatility is 30% per annum, and the time to expiration is 3 months?
4. Put-call Parity. Using the result of Problem 3, calculate the price of a European put option.