Q1. Use the European put call parity to find the condition for the European put the European call to have the identical price.
For Q2Q5, use the following information.
A European call option and a European put option on a stock both have a strike price of $140 and expire in 7 months. Currently, the call price is $20 and the put price is $12 in the market. The risk-free rate is 5% per annum, and the current stock price is $145. Identify the arbitrage opportunity open to the trader. All the interest rates are with continuous compounding.
Q2: Take the call option prices as given and invoke the appropriate putcall parity to find the arbitragefree theoretical price of the put option. This may not be the same as the put market price given in the above.
Q3: Is the put market price ($12) greater or smaller than the arbitragefree put price in Q2? Should you buy the put at $12 or not?
Q4: List the actions that would lock in a sure profit from the apparent mispricing. Create an arbitrage table to show that the net cash flows are nonnegative and have at least one positive to showan arbitrage profit. Hint: Replicate the arbitrage table from the class session.
Hint: If you take a short position of the stock given in the question, the cash flow will be $145 today and S in 7 months.
Q5: If both options above were American options, is the American putcall parity violated?
