Question

1. A trader creates a long butterfly spread from options with strike prices of $90, $100, and $110 per share by trading a total of 20 option contracts (buy 5 contracts at $90, sell 10 contracts at $100 and buy 5 contracts at $110). Each contract is written on 100 shares of stock. The options are worth $15, $18, and $22 per share of stock, respectively.

a) What is the value of the butterfly spread at maturity as a function of the then stock price?

b) What is the profit of the butterfly spread at maturity as a function of the then stock price? Make sure to derive the exact range of then stock prices where the trade is profitable.

Answer 1

		Cash flow for premium
	Buy(Long) Call5 contracts(500 shares) at Strike Price $90	$                  (7,500)	(15*500)
	Sell(Short)Call 10 contracts(1000 shares) at Strike Price $100	$18,000	(18*1000)
	Buy (Long)Call5 contracts(500 shares) at Strike Price $110	$               (11,000)	(22*5000
	Net Cash flow for premium	$                     (500)
	VALUE OF BUTTERFLY OPTION AT MATURITY:
		Gain (Loss) per share			Total Gain (Loss)
		A	B	C	D=A*500	E=B*1000	F=C*500	G=D+E+F
	Price at Expiration	Long CallStrike$90	Short Callstrike $100	LongCall Strike $110	Long Call Strike$90	Short Callstrike $100	Long Call Strike $110	Net gain/(Loss)
	$85	$0	$0	$0	$0	$0	$0	$0
	$86	$0	$0	$0	$0	$0	$0	$0
	$87	$0	$0	$0	$0	$0	$0	$0
	$88	$0	$0	$0	$0	$0	$0	$0
	$89	$0	$0	$0	$0	$0	$0	$0
	$90	$0	$0	$0	$0	$0	$0	$0
	$91	$1	$0	$0	$500	$0	$0	$500
	$92	$2	$0	$0	$1,000	$0	$0	$1,000
	$93	$3	$0	$0	$1,500	$0	$0	$1,500
	$94	$4	$0	$0	$2,000	$0	$0	$2,000
	$95	$5	$0	$0	$2,500	$0	$0	$2,500
	$96	$6	$0	$0	$3,000	$0	$0	$3,000
	$97	$7	$0	$0	$3,500	$0	$0	$3,500
	$98	$8	$0	$0	$4,000	$0	$0	$4,000
	$99	$9	$0	$0	$4,500	$0	$0	$4,500
	$100	$10	$0	$0	$5,000	$0	$0	$5,000
	$101	$11	($1)	$0	$5,500	($1,000)	$0	$4,500
	$102	$12	($2)	$0	$6,000	($2,000)	$0	$4,000
	$103	$13	($3)	$0	$6,500	($3,000)	$0	$3,500
	$104	$14	($4)	$0	$7,000	($4,000)	$0	$3,000
	$105	$15	($5)	$0	$7,500	($5,000)	$0	$2,500
	$106	$16	($6)	$0	$8,000	($6,000)	$0	$2,000
	$107	$17	($7)	$0	$8,500	($7,000)	$0	$1,500
	$108	$18	($8)	$0	$9,000	($8,000)	$0	$1,000
	$109	$19	($9)	$0	$9,500	($9,000)	$0	$500
	$110	$20	($10)	$0	$10,000	($10,000)	$0	$0
	$111	$21	($11)	$1	$10,500	($11,000)	$500	$0
	$112	$22	($12)	$2	$11,000	($12,000)	$1,000	$0
	$113	$23	($13)	$3	$11,500	($13,000)	$1,500	$0
	$114	$24	($14)	$4	$12,000	($14,000)	$2,000	$0
	$115	$25	($15)	$5	$12,500	($15,000)	$2,500	$0
	Value and Profit of Butterfly Spread Maturity as a function of stock
	Price at Expiration		A	B=A-500
		Stock Price	Value	Profit	(Value minus Premium)
		$85	$0	($500)
		$86	$0	($500)
		$87	$0	($500)
		$88	$0	($500)
		$89	$0	($500)
		$90	$0	($500)
		$91	$500	$0
		$92	$1,000	$500
		$93	$1,500	$1,000
		$94	$2,000	$1,500
		$95	$2,500	$2,000
		$96	$3,000	$2,500
		$97	$3,500	$3,000
		$98	$4,000	$3,500
		$99	$4,500	$4,000
		$100	$5,000	$4,500
		$101	$4,500	$4,000
		$102	$4,000	$3,500
		$103	$3,500	$3,000
		$104	$3,000	$2,500
		$105	$2,500	$2,000
		$106	$2,000	$1,500
		$107	$1,500	$1,000
		$108	$1,000	$500
		$109	$500	$0
		$110	$0	($500)
		$111	$0	($500)
		$112	$0	($500)
		$113	$0	($500)
		$114	$0	($500)
		$115	$0	($500)