Question

A stock is trading at $58. You believe there is a 70% chance the price of the stock will increase by 10% over the next 3 months. You believe there is a 20% chance the stock will drop by 10%, and you think there is only a 10% chance of a major drop in price of 20%. At-the-money 3-month puts are available at a cost of $730 per contract. What is the expected dollar profit for a writer of a naked put at the end of 3 months?

Answer 1

Answer: $498

Explanation:

A Put is an option that will only be exercised if the price of the underlying security which is the stock in this case, falls below the current price of $58.

This means that we will not include the 70% chance of increase in our calculation.

In a contract, there are 100 shares.

Expected profit = Contract price - (Prob. of dropping by 10% * 10% of stock) - (Prob. of dropping by 20% * 20% of stock)

= 730 - ( 20% * 10% * 58 * 100) - (10% * 20% * 58 * 100)

= 730 - 116 - 116

= $498