You buy a put option with a strike price of $110 for $7 and sell a put option with a strike price of $95 for $2 on the same stock (same expiry). The contract size (multiplier) is 1 share per option contract.

What is the maximum profit at the expiry in dollars?

Question

You buy a put option with a strike price of $110 for $7 and sell a put option with a strike price of $95 for $2 on the same stock (same expiry). The contract size (multiplier) is 1 share per option contract.

What is the maximum profit at the expiry in dollars?

BlackTom AI · Accepted Answer

First, lay out the positions and the cash flows: you buy a put with strike 110 for 7 and you sell a put with strike 95 for 2 on the same stock and expiry. The net premium paid is 7 - 2 = 5 dollars (a net debit). Now, determine the payoff at expiry for different spots S: - If S >= 110: both puts are out of the money (110-S <= 0 and 95-S <= 0). The payoff from the long 110 put is 0, the payoff from the short 95 put is 0, so total payoff = 0. Your profit is payoff minus the net premium: 0 - 5 = -5. - If 95 <= S < 110: the long 110 put is in the money with payoff 110 - S, while the short 95 put remains out of the money (95 - S <= 0), so total payoff = 110 - S. Profit = (110 - S) - 5. Since this expression decreases as S increases, it is maximized at the smallest S in this range, i.e., S = 95, giving profit = (110 - 95) - 5 = 15 - 5 = 10. - If S < 95: both puts are in the money. The long 110 put payoff is 110 - S, the short 95 put payoff is -(95 - S). Total payoff = (110 - S) - (95 - S) = 15. Then profit = 15 - 5 = 10. Summarizing the profit across all possible S: in the S < 95 region, profit is 10; in the 95 <= S < 110 region, profit ranges from 10 down to something smaller as S rises, and in S >= 110 region, profit is -5. Therefore, the maximum possible profit at expiry is 10 dollars. This outcome makes intuitive sense: the combination creates a bull-ish put spread (a bear-ish collar-like structure) with a fixed net debit of 5, and the maximum payoff differential between the two puts caps the profit at 10 when the stock price ends at or below 95. The net premium of 5 is the amount you must earn back via the spread's intrinsic values to reach the maximum.

You buy a put option with a strike price of $110 for $7 and sell a put option with a strike price of $95 for $2 on the same stock (same expiry). The contract size (multiplier) is 1 share per option contract. What is the maximum profit at the expiry in dollars?数值题

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