Put Options in 10 Minutes
A put option gives you the right, but not the obligation, to sell a share at a fixed strike price. Puts gain value when the stock falls, which is why investors use them as insurance. These notes cover how puts work, their payoff and profit at expiration, and where valuation comes in.
What you will learn
- What a put option is: the right to sell at the strike price
- How to calculate put payoff and profit at expiration
- How to find the break-even price for a put buyer
- When a put is in, at, or out of the money
- How puts work as insurance on a stock you already own
The formulas
- K
- strike (exercise) price
- S_T
- stock price at expiration
- Premium
- price paid for the put
- Break-even S_T
- stock price at which the buyer neither gains nor loses
Worked example
You buy a put with a $50 strike for a $3 premium. What is your payoff and profit if the stock is at $40 at expiration? What if it is at $55?
- At $40: payoff = max(50 − 40, 0) = $10.
- Profit = $10 − $3 = $7 per share.
- Break-even = $50 − $3 = $47.
- At $55: payoff = max(50 − 55, 0) = $0, so you lose the $3 premium.
Answer: At $40 you make $7 per share ($700 on a standard 100-share contract). At $55 the put expires worthless and you lose $3 per share. You break even at $47.
Common questions
How does a put option work?
You pay a premium for the right to sell a stock at the strike price until expiration. If the stock falls below the strike, you can sell high while the market price is low, so the put pays off. If the stock stays above the strike, you let it expire and lose only the premium.
What is the maximum loss and gain on a put option?
For a put buyer, the most you can lose is the premium. The most you can gain is the strike price minus the premium, which happens if the stock falls to zero. Put sellers face the mirror image: limited gain, large potential loss.
When is a put option in the money?
A put is in the money when the stock price is below the strike, at the money when they are equal, and out of the money when the stock is above the strike. Only in-the-money puts have a positive payoff at expiration.
What is the difference between a put and a call option?
A call gives the right to buy at the strike price and pays off when the stock rises. A put gives the right to sell at the strike price and pays off when the stock falls. Both cost a premium, and buyers of either can lose no more than that premium.