Question

You sell one Amazon call option and sell one Amazon put option. The exercise price is $120, the call premium is $2.50, and the put premium is $7.25. Your strategy will pay off only if the stock price is ____ at maturity.

a) Between $112.75 and $127.25
b) Between $117.50 and $127.25
c) Between $110.25 and $129.75
d) Either lower than $110.25 or higher than $129.75
e) None of the above

Answer 1

The correct payoff range for selling one Amazon call and put option with given premiums is between $112.75 and $122.50. None of the given choices in the question match this range; therefore, the correct answer would be 'e) None of the above'.

Step-by-step explanation:

When you sell a call option, you receive the premium but may have to sell the underlying stock at the exercise price if the buyer exercises the option. In this case, if Amazon's stock price is above $120 at maturity, you will have to sell the stock at $120, but you have already gained $2.50 from the call premium, so your break-even price is $122.50 on the upside. Conversely, when you sell a put option, you also receive the premium, but you may have to buy the stock at the exercise price if the buyer exercises the option. If the stock price is below $120, you will have to buy the stock at $120, but you have the $7.25 from the put premium, leading to a break-even price of $112.75 on the downside.

Hence, your combined strategy involving both options will pay off if the stock price is between $112.75 and $122.50 at maturity. This is because if the stock stays within this range, neither option is likely to be exercised, and you keep both premiums. However, the payoffs are incorrect in the question's answer choices. There is a mistake as none of the given choices correctly represent the payoff range.

Answer 2

Upon selling a call and a put option with the same exercise price, the break-even points are found by adjusting the exercise price by the premiums. The profitable range should be between these points, $112.75 and $122.50; however, none of the provided options match this range, indicating a potential error in the question.

Step-by-step explanation:

When you sell a call option and a put option at the same exercise price, you are constructing an options trading strategy known as a short strangle. To determine the range in which this strategy is profitable, calculate the break-even points by subtracting the put premium from the exercise price and adding the call premium to the exercise price.

The break-even points are:

• Lower break-even: Exercise price – Put premium = $120 – $7.25 = $112.75
• Upper break-even: Exercise price + Call premium = $120 + $2.50 = $122.50

Therefore, your strategy will pay off only if the stock price is between $112.75 and $122.50 at maturity. However, none of the provided options exactly match this range, suggesting that the correct answer might not be listed or that there may be an error in the question. Generally, the correct range for a short strangle's profit would be between the two break-even points.