Question

• Short currency strangle . Call option premium - $0.03/€, Put option premium - $0.028€ Call option strike price = $1.15/€, Put option strike price - $1.05/€ Option contract size = €62,500 Draw graphs of call option, put option, and straddle • Mark BE point and Strike prices • Mark each premium $1.05/€ $1.10/€ $1.15/€ | $1.20/€ $1.25/€ $1.30/€ Spot exchange rate Does holder exercise? Sell call option Holder's net profit per unit Seller's net profit per unit Does holder exercise? Sell put option Holder's net profit per unit Seller's net profit per unit Net profit Net profit per unit

Answer 1

Solution:

Buyers(holders) of the option pay premium to the writers of the option.

Sellers(writers) of the options receive premium from the holders of the option.

Holder(Buyer) of call option exercise a call option only when the spot exchange rate is higher than the strike price.

Holder(Buyer) of put option exercise a put option only when the spot exchange rate is lower than the strike price.

Net profit of buyer of call option = max(0, spot price - strike price) - premium paid

Net profit of seller of call option = min(o, strike price - spot price) + premium received

Net profit of buyer of put option = max(o, strike price - spot price) + premium paid

Net profit of seller of put option = min(0, spot price - strike price) + premium received

Spot Exchange Rate($/€)		1.05	1.1	1.15	1.2	1.25	1.3
Sell Call Option	Does holder exercise?	no	no	no	yes	yes	yes
	Holder's net profit per unit	-0.03	-0.03	-0.03	-0.08	-0.13	-0.18
	Sellers's net profit per unit	0.03	0.03	0.03	-0.02	-0.07	-0.12
Sell Put Option	Does holder exercise?	no	no	no	no	no	no
	Holder's net profit per unit	-0.02	-0.02	-0.02	-0.02	-0.02	-0.02
	Sellers's net profit per unit	0.02	0.02	0.02	0.02	0.02	0.02
Net Profit		0.05	0.05	0.05	-4.51E-17	-0.05	-0.1

Break-even point for the seller of call option is when the spot price is equal to the strike price + premium received.

Break-even point for the seller of put option is when the spot price is equal to the strike price - premium received.

So in this case break even point on

short call option is 1.15+0.03 = 1.18 dollar/euro.

short put option id 1.05-0.02=1.03 dollar/euro.

There are 2 Break even points for a short strangle.

Lower Strike Price - Sum of premium received = 1.05 - (0.03+0.02) = 1 dollar/euro

Higher Strike Price + Sum of premium received = 1.15 + (0.02+0.03) = 1.2 dollar/euro

Graphs

	Write a Call					Write a Put
Spot Price	Holder Exer	Gross Gain	Premium	Net Gain		Holder E/L	Gross Gain	Premium	Net Gain		NET PROFIT
0.8	no	0	0.03	0.03		yes	-0.25	0.02	-0.23		-0.20
0.85	no	0	0.03	0.03		yes	-0.2	0.02	-0.18		-0.15
0.95	no	0	0.03	0.03		yes	-0.1	0.02	-0.08		-0.05
1	no	0	0.03	0.03		yes	-0.05	0.02	-0.03		0.00
1.05	no	0	0.03	0.03		no	0	0.02	0.02		0.05
1.1	no	0	0.03	0.03		no	0	0.02	0.02		0.05
1.15	no	0	0.03	0.03		no	0	0.02	0.02		0.05
1.2	yes	-0.05	0.03	-0.02		no	0	0.02	0.02		0.00
1.25	yes	-0.1	0.03	-0.07		no	0	0.02	0.02		-0.05
1.3	yes	-0.15	0.03	-0.12		no	0	0.02	0.02		-0.10
1.35	yes	-0.2	0.03	-0.17		no	0	0.02	0.02		-0.15

SHORT CALL OPTION

Net Gain 0.05 0.75 0.95 1.25 -0.02 -0.05 -0.15

breakeven point in this is 1.18 dollar/euro.

SHORT PUT OPTION

Net Gain 0.05 0.75 0.85 0.95 -0.05 -0.15 -0.25

breakeven point for this is 1.03 dollar/euro

SHORT SRANGLE

NET PROFIT 0.10 0.05 0.00 0.75 0.85 0.95 1.05 1.15 1.25 1.35 1.45 -0.05

breakeven points are 1 dollar/euro and 1.2 dollar/euro.