Question

On April 6, 2020, the price of Apple Inc. stock was 262.43. Assume you observe the following prices of European PUTS on the stock:   

Strike	Premium
$245	$6.16
$250	$5.15
$255	$12.22
$260	$13.45

For one pair of options, the relationship p ( K 2 ) − p ( K 1 ) ≤ K 2 − K 1 , f o r K 1 ≤ K 2DOES NOT HOLD and thus arbitrage opportunities exist. The arbitrage strategy: buy option with strike price____ _, sell option with strike price_____ . Minimum profit per share is:______ . Notes: Answer all the questions with exactly two decimal places.

Answer 1

Strike price	Premium	Difference in price	Difference in premium
245	6.16
250	5.15	5	1.01
255	12.22	5	7.07	So here the arbitrage opportunity exists.
260	13.45	5	1.23
So the minimum profit will be 2.07 always (7.07-5) as illustrated with an example below.
Note: we see that there is a difference of $5 at every strike price we compare with the other but in case of premium if we compare
the strike prices shown above we see the differnce in premium is more then the difference in strike price and hence the arbitrage opportunity exists. So if we buy put at $250 and sell the put at $255 then the net premium inflow will be $7.07.
Ilustration to prove minimum profit of $2.07
Maturity price	P+ at 250	P- at 255	Payoff	working	Net premium inflow	Profit/(loss)
240	Exercise in favour	Exercise against us	5	(250-240)+(240-255)	7.07	2.07
252	lapse	Exercise against us	3	255-252	7.07	4.07
260	lapse	Exercise in favour	5	260-255	7.07	2.07

Buy price $250, Sell price $255, minimum profit $2.07