Question

Today’s price of Delta is $150 per share. You are neither bullish nor bearish about Delta, but you believe that the share price will not move by a lot in the near future. To implement your view, you decide to sell a straddle with one month until maturity. An option dealer provides you quotes on one-month Delta options. For a call option with a strike of $150, the dealer quotes you a price of $4.32. For a put option with a strike of $150, the dealer quotes you a price of $4.32. The c.c. risk-free rate is zero. What is the profit to the short straddle if Delta trades at $200 per share in one month?

There are 2 breakevens, what is the high and what is the low? (There should be two answers, one for high and one for low)

Answer 1

Profit of short straddle = profit on short call option + profit on short put option

If the share is $200 at expiration, the short put option will not be exercised by the buyer as it is out of the money. Profit on short put option = premium received = $4.32

If the share is $200 at expiration, the short call option will be exercised by the buyer as it is in the money. Profit on short call option = (option strike price - share price at expiration) + premium received

Profit on short call option = ($150 - $200) + $4.32 = -$45.68

Profit of short straddle = -$45.68 + $4.32 = -$41.36

Upper breakeven = straddle strike price + total premium received

Lower breakeven = straddle strike price - total premium received

total premium received = premium received on short call option + premium received on short put option

total premium received = $4.32 + $4.32 = $8.64

Upper breakeven = $150 + $8.64 = $158.64

Lower breakeven = $150 - $8.64 = $141.36