Question

The following option prices were observed in the Listed Options Quotations section of the Wall Street Journal for Walt Disney on Tuesday February 27.

			Calls-Last		Puts-Last
Close	Strike Price	March	April	May	March	April	May
121.375	115	7.75	9.875	14.875	1.125	2.875	5.125
121.375	120	4.125	6.875	10.875	2.50	4.75	7.375
121.375	125	2.125	4.375	8.25	5.50	6.875	9.375
121.375	130	0.625	2.375	5.50	9.25	9.75	11.125

The time-to-expiration in March is 21 days, in April 52 days and in May 112 days. The continuously compounded risk free rate is 0.0535. The standard deviation of returns is 0.28. The stock price does not pay dividends.

a. Construct a bear money spread using the April 120 and 130 puts. Hold until the options expire. Determine the profits and graph the results. Identify the breakeven stock price at expiration and the maximum possible profit and maximum loss.

b. Construct the put bear money spread constructed in part(a) to a bear call money spread.

c. Are there any arbitrage opportunities present in the data. Carefully explain how to identify and exploit any potential arbitrage opportunities.

Answer 1

a)

Payoff chart from bear put spread is shown below

Price	100	105	110	115	120	125	130	135	140	145	150
Payoff 130P Long	30	25	20	15	10	5	0	0	0	0	0
Payoff 120P Short	-20	-15	-10	-5	0	0	0	0	0	0	0
Payoff combined	10	10	10	10	10	5	0	0	0	0	0
Profit after costs	5	5	5	5	5	0	-5	-5	-5	-5	-5

Break even: $125

Maximum profit: $5

Maximum loss: $5

b)

Payoff chart from bear call spread is shown below

Price	100	105	110	115	120	125	130	135	140	145	150
Payoff 130C Long	0	0	0	0	0	0	0	5	10	15	20
Payoff 120C Short	0	0	0	0	0	-5	-10	-15	-20	-25	-30
Payoff combined	0	0	0	0	0	-5	-10	-10	-10	-10	-10
Profit after costs	4.5	4.5	4.5	4.5	4.5	-0.5	-5.5	-5.5	-5.5	-5.5	-5.5

Combined chart-

c) Based on the combined chart, we infer that a bear put spread always yields a higher payoff than the bear call spread. If a bull call spread is taken with a bear put spread, profits will be realized without any risk or downside.

Price	100	105	110	115	120	125	130	135	140	145	150
Payoff 130C Short	0	0	0	0	0	0	0	-5	-10	-15	-20
Payoff 120C Long	0	0	0	0	0	5	10	15	20	25	30
Payoff 130P Long	30	25	20	15	10	5	0	0	0	0	0
Payoff 120P Short	-20	-15	-10	-5	0	0	0	0	0	0	0
Payoff combined	10	10	10	10	10	10	10	10	10	10	10
Profit after costs	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5