Question

A short straddle position is formed by selling a call and a put on the same underlying asset, with the same exercise price and same expiration date. Given the following quotations from April 25, 2018 for a pair of Rio Tinto call and puts, answer the questions below. Strike price for both options: 3800 pence per share Option expiration date: July 21, 2018 Call price = 85 pence per share Put price = 75 pence per share

a) Plot the payoff and profit diagrams for the short straddle position whose components are given above. Make sure that your plots are as informative as positive.

b) suppose that the investor holds the short straddle position till option expiration and that, on July 21, 2018, Rio Tinto stock closes on 4000 pence. what is the net return (in pence) per share to the investor from the investment?

Answer 1

K: strike price

Short straddle: 1 short call (K=3800) + 1 short put (K=3800)

c: call premium received per option = 85

p: put premium received per option = 75

Total premium received = 85+75 = 160

S: spot price on expiry

short call pay-off = -max(S-K,0) = -max(S-3800,0)

short put pay-off = -max(K-S,0) = -max(3800-S,0)

Profit = (short call pay-off) + (short put pay-off) + premium received

a)

Stock price	Short call payoff	Short put payoff	Premium received	Total profit
2800	0	-1000	160	-840
2900	0	-900	160	-740
3000	0	-800	160	-640
3100	0	-700	160	-540
3200	0	-600	160	-440
3300	0	-500	160	-340
3400	0	-400	160	-240
3500	0	-300	160	-140
3600	0	-200	160	-40
3700	0	-100	160	60
3800	0	0	160	160
3900	-100	0	160	60
4000	-200	0	160	-40
4100	-300	0	160	-140
4200	-400	0	160	-240
4300	-500	0	160	-340
4400	-600	0	160	-440
4500	-700	0	160	-540
4600	-800	0	160	-640
4700	-900	0	160	-740
4800	-1000	0	160	-840

b) If stock closes at 4000, net profit = -40 pence

Payoff short call = -max(4000-3800,0) = -200

Payoff short put = -max(3800-4000,0) = 0

Premium received = 160

net profit = -200+0+160 = -40 pence