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A stock is trading at $59. You believe there is a 80% chance the price of the stock will increase by 15% over the next 3 months. You believe there is a 5% chance the stock will drop by 5%, and you think there is only a 15% chance of a major drop in price of 30%. At-the-money 3-month puts are available at a cost of $740 per contract. What is the expected dollar profit for a writer of a naked put at the end of 3 months?

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Answer:

$459.75

Explanation:

Given that :

Trade price = $59

80% chance that stock increases by 15%

5% chance that stock drops by 5%

15% chance of a major drop by 30%

(80% + 5% + 15%) = 100

Cost per contract = $740

Expected dollar profit: Σx*p(x)

-[0.8max(0,59 - (59 * (1+ 0.1))) * 100

-[0.8max(0, - 5.9)) * 100

-[0.8(0) *100) = 0

[0.05max(0,59 - (59 * (1 - 0.05))) * 100

= 0.05(295) = 14.75

[0.15max(0,59 - (59 * (1 - 0.3))) * 100

= 0.15(1770) = 265.5

-(0 + 14.75 + 265.5) + 790

- 280.25 + 740

= $459.75

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