Put–call parity asserts that the sum of the prices of the stock and put must equal the prices of the call and the bond. If they do not, an arbitrage opportunity exists and you can generate a risk-free return. Given the following information,
Price of the stock                                                                                  $50.00
Interest rate                                                                                                  5%
Price of a $50 bond discounted at the current interest rate           $47.62
Price of a call to buy the stock at $50                                                   $4.38
Price of a put to sell the stock at $50                                                    $4.00
an arbitrage opportunity exists. Unfortunately, you construct the wrong positions (do everything backwards). Verify that you always lose at the following prices of the stock: $40, $45, $50, $55, and $60.

2.Black-Scholes demonstrates that the value of a put option increases the longer the time to expiration. Currently the price of a stock is $100 and there are two put options to sell the stock at $100. The three-month option sells for $7.00 and the six-month option sells for $4.50. a) What would you do and why? b) How much do you earn or lose after three months at the following prices of the underlying stock ($85, $90, $95, $100, $105, and $110)? Assume the worst-case scenario. c) Is there any reason to anticipate earning a higher return than your answers in (b)?