CFA Level IDerivativesMedium
An investor sells a European put option with a strike price of $70 for a premium of $4. At expiration, the underlying asset's price is $65. What is the profit or loss from this position?
- ALoss of $5
- BProfit of $5
- CProfit of $4
- DLoss of $1
Show answer & explanationAnswer & explanation
Correct answer: D. Loss of $1
For a short put option, the payoff to the option buyer is max(0, Strike Price - Spot Price). The profit for the seller is the premium received minus this payoff. If the option is exercised, the seller incurs a loss equal to the difference between the strike and spot, less the premium.
Why the other options are wrong
- A. This is the payoff to the buyer, which is the loss for the seller if no premium was received.
- B. This incorrectly calculates the profit if the option is in-the-money.
- C. This would be the profit if the option expired out-of-the-money.
Short Put Option Profit
The profit for a short put option is the premium received minus the payoff to the buyer (Strike Price - Spot Price, if positive).
- Payoff to buyer = max(0, Strike Price - Spot Price)
- Profit for seller = Premium - Payoff to buyer
- Seller's maximum profit is the premium received if the option expires out-of-the-money
- Seller's maximum loss is limited but can be substantial as the underlying price approaches zero
Memory trick: Short put: Collect first, then pay if put to the test!