Question

A European call option and put option on a stock both have a strike price of $20 and an expiration date in three months. Both sell for $3. The risk-free interest rate is 10% per annum, the current stock price is $19, and a $1 dividend is expected in one month. Is there an arbitrage opportunity? If there is an arbitrage opportunity, clearly state what condition must be satisfied to eliminate the arbitrage opportunity. What is the strategy followed to make a profit from the arbitrage opportunity? What is the profit expressed as a present value?

Answer 1

Answer:

1a arbitrage opportunities exist 1b. The law of one price 1c. net profit =$0.843

Explanation:

1a.In order to see if there are any arbitrage opportunities the put call parity will be used

p+s-p(div)=c+x*e^-r*t

3+19-(1/1) =3+20*e^-0.1*1/12

21.0083  =22834

Arbitrage opportunities exist as the put and call have different prices

1b. The law of one price must be satisfied meaning the prices must be same

1c. The strategy is to buy a put since it is under-priced and short sell a call

so

$3+$19-$3=19

Pv =19*e^0.1*1/12=$19.159

Only exercise the put if the the price is less than $20 and get $20 other wise sell the put option $20 so the either way the result is $20

PV = $20*e^0.1*1/12

    =19.834

Net profit= 19.834-19

                =$0.834