Question

Disney, ticker DIS, closed at around $110 on 5/8. You believe its share price is going to stay in a narrow range around $110 for the next year. To speculate on your belief, you decide to sell a straddle. The straddle strategy is entering the same position in both a call and a put sharing the same underlying, expiration, and strike price. When you sell a straddle, you are selling both the call and the put.

The price of a call option with a one-year expiration written on Disney with an exercise price of $110 is $17. The current stock price of Disney is $110 and the risk-free rate is 10% per year.

(a) What must be the price of the one-year put on the same stock with the same strike price?

(b) Construct your position table of the selling of the straddle strategy. Again, you are selling both the call and the put with the same strike price of $110.

(c) Plot your position diagram for your strategy. Plot one line for the payoff and one line for the profit. To figure out your profit, use the call price given ($17) and the put price you solved in part (a).

(d) At what stock price at expiration (S_T) do you make the most money? And what is your maximum profit on this strategy?

(e) What are the breakeven prices for this strategy, that is, how far can the stock price move in either direction before you lose money?

Answer 1

(a) The put-call parity is given by c + X*e^(-r*t) = p +S(0)

X is the strike price = 110

S(0) is the current stock price = 110

c is the call option price = 17

The put option price is given by the put-call parity

p =C + X*e^(-r*t)-S(0)

p = 17+ 110*e^(-0.1*1) - 110

p = 6.532

(b)

Stock price	Payoff short call strike $110	Payoff short put strike $110	Combined position
80	17	-23.468	-6.468
81	17	-22.468	-5.468
82	17	-21.468	-4.468
83	17	-20.468	-3.468
84	17	-19.468	-2.468
85	17	-18.468	-1.468
86	17	-17.468	-0.468
86.47	17	-16.998	0
87	17	-16.468	0.532
88	17	-15.468	1.532
89	17	-14.468	2.532
90	17	-13.468	3.532
91	17	-12.468	4.532
92	17	-11.468	5.532
93	17	-10.468	6.532
94	17	-9.468	7.532
95	17	-8.468	8.532
96	17	-7.468	9.532
97	17	-6.468	10.532
98	17	-5.468	11.532
99	17	-4.468	12.532
100	17	-3.468	13.532
101	17	-2.468	14.532
102	17	-1.468	15.532
103	17	-0.468	16.532
104	17	0.532	17.532
105	17	1.532	18.532
106	17	2.532	19.532
107	17	3.532	20.532
108	17	4.532	21.532
109	17	5.532	22.532
110	17	6.532	23.532
111	16	6.532	22.532
112	15	6.532	21.532
113	14	6.532	20.532
114	13	6.532	19.532
115	12	6.532	18.532
116	11	6.532	17.532
117	10	6.532	16.532
118	9	6.532	15.532
119	8	6.532	14.532
120	7	6.532	13.532
121	6	6.532	12.532
122	5	6.532	11.532
123	4	6.532	10.532
124	3	6.532	9.532
125	2	6.532	8.532
126	1	6.532	7.532
127	0	6.532	6.532
128	-1	6.532	5.532
129	-2	6.532	4.532
130	-3	6.532	3.532
131	-4	6.532	2.532
132	-5	6.532	1.532
133	-6	6.532	0.532
133.53	-6.53	6.532	0
134	-7	6.532	-0.468
135	-8	6.532	-1.468
136	-9	6.532	-2.468
137	-10	6.532	-3.468
138	-11	6.532	-4.468
139	-12	6.532	-5.468
140	-13	6.532	-6.468

(c)

(d)

From the table, if the stock price at maturity T is equal to $110, we make a maximum profit equal to $23.532

(e) Break-even point is the point at which there is no profit, no loss. From the table, when the stock price at maturity equals $86.47 and $133.53 there is a break-even point. ie. the stock can move in either direction between these 2 points before you lose money.