Consider a put and a call both on the same underlying stock

Consider a put and a call, both on the same underlying stock that has present price of $34. Both options have the same identical strike price of $32 and time-to-expiration of 200 days. Assume that there are no dividends expected for the coming year on the stock, the options are all European, and the interest rate is 10%. If the put premium is $7.00 and the call premium is $12.00, which portfolio would yield arbitrage profits? Hint: Check your answer with an arbitrage table.

buy the put , buy the call, sell stock, sell a bond

buy the stock, buy the bond, write the put, write the call

buy the call, buy a bond, write the put, sell stock

buy a put, buy stock, write the call, sell bond

no arbitrage is available for these asset prices

Solution

Answer : buy the call,buy a bond,write the put,sell stock

For call option:

Current price of stock = $34

Call strike price = $32

for this we wiil excercise the call option since strike price is less than current price.

Intrinsic value = $34 - $32 = 2

For put option

Current price of stock = $34

Put strike price = $32

for this we wiil not excercise the call option since strike price is less than current price.

Intrinsic value = 0

So we will write the put option.

Hence,

Strategy is Buy the call,Buy a bond,Write the put,sell stock to maximize portfolio profits.