Use the European put­call parity to find the condition

Use the European put­call parity to find the condition

Subject: Business    / Finance   
Question
Q1. Use the European put­call 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?