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 $32. Both options have the same identical strike price of $26 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 $4.00 and the call premium is $9.00, which portfolio would yield arbitrage profits? Hint: Check your answer with an arbitrage table.

$0.43

$1.37

$1.42

$1.47

$2.32

Solution

According to call put theory

9 + 26/1.10^200/365 = 4 + 32

RHS = 36

LHS = 33.677

arbitrage opportunity = 36 - 33.677 = 2.32