1 .A stock sells for $52 per share, and the 6-month European call on the stock with a strike price of $50 sells for $2.50. The stock is not expected to pay any dividends in next six months. The risk free interest rate is 4% per annum, continuously compounded. How can you get a free lunch from the market? Describe your transactions clearly.
2. An at-the-money three-month European call option on a non-dividend-paying stock has a market price of $1.27. The stock price is $20 and the risk-free interest rate is 8% per annum, with continuous compounding. Verify that the implied volatility is about 27%.
3. A European call option and put option on a stock both have a strike price of $20 and an expiration date in three months. Both sell for $3. The risk-free interest rate is 10% per annum, the current stock price is $19, and no dividend is expected in three months. How can you make a free lunch in these markets?
4. A non-dividend-paying stock sells for $42 per share. The continuously compounded risk-free interest rate is 6% per annum, and the volatility of the stock price is 30% per annum. Use the Black-Scholes-Merton model to determine the price of a 3-month European call on the stock with a strike price of $40.