option and a European

the total interest amount
November 7, 2019
comparing leasing versus purchasing
November 7, 2019

option and a European

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?

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