# How do I extract the arbitrage?

You are looking at a particular stock ticker and its options. You can go long or short on any quantity of the following instruments:

• Each unit of stock is priced at \$10. • A call on the stock with strike price at \$15 is priced at \$2. • A put on the stock with strike price at \$15 is priced at \$6. Is there an arbitrage opportunity here? If so, how do you extract the arbitrage? • I think you should be able to check this with put-call parity. Since you haven't given any values of r and T we should have from C + K*$exp$(-rt) = P + S that 2 + 15*$exp$(-rt) = 6 + 10. Meaning that was as long as r*t != log(15/14)~=0.03 there should be an arbitrage opportunity. Jun 29 at 7:38 ## 1 Answer It may be possible with a synthetic short with a long underlying stock. Buy 1 put and sell 1 call for a debit of$4

Buy 1 stock for a debit of $10 Net debit =$14

On expiry, if stock is:

\$0: Call and Stocks are \$0, Put is worth \$15, net \$1 gain.

\$10 (unchanged): Call is \$0, Stock is \$10, Put is \$5, net \$1 gain. \$15 (worthless options): Call and Put are \$0, Stock is \$15, net \$1 gain. \$X, X>\$15 : Put is \$0, Stock is \$X, Call is \$15-\$X (it's a short call position). This nets out to \$15, take away the initial debit of - \$14, and you net \$1 gain again.

There may be other opportunities, this is just one I found.

• Since you have an initial debt of 14 you also have to take into account the time horizon and interest rates to see if there is indeed an arbitrage opportunity here. Will borrowing 14 for the duration of the maturity of the options costs you 1 then there would be no arbitrage. Jun 29 at 7:30