Question

Put options with strikes of 70, 75, and 80 have option premiums of 4.00, 8.00, and 11.00, respectively. Given this information, in which way can you undertake an arbitrage?

Answer 1

Here price gap between exercise price is 5$ , however there is difference in price gap of premiums
For 70 PE it is 4$ for 75 PE it is 8$ and for 80PE is 11$ which should had been 12$
Thus there is arbitrage opportunity

Buy a P(70) and a P(80), Short two P(75)

Table showing pay off

Price at expiry	Bought PE @70	2 short PE @75	Bought PE @80	Premium ([2*8] - (4+11))	Net profit and loss
60	10	-30	20	1	1
61	9	-28	19	1	1
62	8	-26	18	1	1
63	7	-24	17	1	1
64	6	-22	16	1	1
65	5	-20	15	1	1
66	4	-18	14	1	1
67	3	-16	13	1	1
68	2	-14	12	1	1
69	1	-12	11	1	1
70	0	-10	10	1	1
71		-8	9	1	2
72		-6	8	1	3
73		-4	7	1	4
74		-2	6	1	5
75		0	5	1	6
76			4	1	5
77			3	1	4
78			2	1	3
79			1	1	2
80			0	1	1
81				1	1
82				1	1
83				1	1
84				1	1
85				1	1
86				1	1
87				1	1
88				1	1
89				1	1
90				1	1