Question

The following prices are available for call and put options on a stock priced at $50. The risk-free rate is 6 percent and the volatility is 0.35. The March options have 90 days remaining and the June options have 180 days remaining. The Black-Scholes model was used to obtain the prices.

	Calls		Puts
Strike	March	June	March	June
45	6.84	8.41	1.18	2.09
50	3.82	5.58	3.08	4.13
55	1.89	3.54	6.08	6.93

Use this information to answer the following questions. Assume that each transaction consists of one contract for 100 shares.

For the following, consider a bull money spread using the March 45/50 calls.

How much will the spread cost?

What is the maximum profit on the spread?

What is the maximum loss on the spread?

What is the profit/loss if the stock price at expiration is $47?

What is the breakeven point?

Answer 1

bull spread can be constructed using call options. Here call option with higher strike price is sold and call option with lower strike price is purchased

Thus cost of strategy = 6.84-3.82 = 3.02

Table showing Payoff

Price as on expiry	Profit on long call	Profit on short call	Net profit/loss
40	-6.84	3.82	-10.66
41	-6.84	3.82	-10.66
42	-6.84	3.82	-10.66
43	-6.84	3.82	-10.66
44	-6.84	3.82	-10.66
45	-6.84	3.82	-10.66
46	-5.84	3.82	-9.66
47	-4.84	3.82	-8.66
48	-3.84	3.82	-7.66
49	-2.84	3.82	-6.66
50	-1.84	3.82	-5.66
51	-0.84	3.82	-4.66
52	0.16	3.82	-3.66
53	1.16	3.82	-2.66
54	2.16	3.82	-1.66
55	3.16	3.82	-0.66
56	4.16	2.82	1.34
57	5.16	1.82	3.34
58	6.16	0.82	5.34
59	7.16	-0.18	7.34
60	8.16	-1.18	9.34

Maximum profit is unlimited , maximum loss is -10.66$

At 47 $ , there will be loss -8.66$

Break even will be at 55$