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
breakeven point in this is 1.18 dollar/euro.
SHORT PUT OPTION
breakeven point for this is 1.03 dollar/euro
SHORT SRANGLE
breakeven points are 1 dollar/euro and 1.2 dollar/euro.
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