Question

Recall that to create a ‘butterfly spread’, an investor buys one unit of an in-themoney call option, buys one unit of an out-of-the money call option, and sells two units of an at-the-money call option. Three European call options with exercise prices of 45, 50, and 55 are currently trading in the market. These options have the same expiration date and are on the same underlying stock. The stock is currently trading at a price of 50. i. Graph the payoff diagram of the butterfly spread at maturity. ii. What view on the future direction of the underlying stock price does an investor who purchases this butterfly spread hold?

Answer 1

QUESTION (i)

Step 1 - Strategy

To create a butterflu spread we will have to

a) Buy one call option of 45 Strike price

b) Sell two call options of 50 Strike price

c) Buy one call option of 55 Strike Price

Step - 2 Calculation of payoff from the strategy at various strike price on expity

	Max(ST-45,0)	-Max(ST-50,0)*2	Max(ST-55,0)
Stock Price on Expiry (ST)	Payoff from buying one call of 45 Strike	Payoff from Selling two call of 50 Strike	Payoff from buying one call of 55 Strike	Total Payoff
40	0	0	0	0
41	0	0	0	0
42	0	0	0	0
43	0	0	0	0
44	0	0	0	0
45	0	0	0	0
46	1	0	0	1
47	2	0	0	2
48	3	0	0	3
49	4	0	0	4
50	5	0	0	5
51	6	-2	0	4
52	7	-4	0	3
53	8	-6	0	2
54	9	-8	0	1
55	10	-10	0	0
56	11	-12	1	0
57	12	-14	2	0
58	13	-16	3	0
59	14	-18	4	0
60	15	-20	5	0

Payoff Diagram of this Strategy

QUESTION (ii)

View on the future direction of underlying stock price

An investor buying a Butterfly calll Spread has a view that stock price will "remain rangebound" , In this scenario investor expects that stock price will remain in the range of 45-55,

Till the stock price of the remains in the range of 45-55 investor will get a positive payoff which is shown in the diagram above