Long Put Option Payoff: Stock Price Below Strike Price

Imagine you’ve bought a kind of insurance policy for a stock you don’t even own yet. This policy is called a long put option. Think of it as securing a guaranteed selling price for a stock, just in case its price falls. This guaranteed price is called the strike price. You pay a small fee upfront to buy this insurance, which is the premium of the option. This insurance policy, your put option, has an expiration date, a specific day when this price guarantee expires.

Now, let’s consider what happens at the expiration date if the stock price has actually fallen, specifically if it’s below the strike price you secured. Let’s say you bought a put option with a strike price of $50 for a particular stock. This means you have the right to sell that stock for $50, regardless of its market price, up to the expiration date. Suppose, when expiration day arrives, the stock is trading at $40.

Because you hold a long put option, you have a very valuable right. You have the right to sell something for $50 that is currently worth only $40 in the market. It’s like having a coupon that lets you sell a $40 item for $50 – you definitely want to use that coupon! This is exactly what happens with a put option when the stock price is below the strike price at expiration. As a rational investor, you will exercise your option.

Exercising your put option means you are enacting your right to sell the stock at the strike price. In our example, you would exercise your right to sell the stock at $50. Since the market price is only $40, for every share covered by your put option, you essentially gain the difference between the strike price and the market price.

Therefore, the payoff for a long put option when the stock price at expiration is below the strike price is calculated as follows: Take the strike price, the guaranteed selling price you secured, and subtract the actual stock price at expiration. This difference represents your profit per share before considering the initial cost you paid for the option itself, the premium.

In our example with a $50 strike price and a $40 stock price at expiration, the payoff is $50 minus $40, which equals $10 per share. So, for each put option contract you hold, which typically represents 100 shares, your payoff would be $10 multiplied by 100, or $1000, before considering the initial premium.

To determine your net profit or loss, you need to subtract the premium you initially paid for the put option from this payoff. Let’s imagine you paid a premium of $2 per share for this put option, or $200 for a contract of 100 shares. Your net profit would then be the $10 payoff per share minus the $2 premium per share, resulting in an $8 net profit per share, or $800 for the contract.

In essence, when the stock price ends up below the strike price at expiration for a long put option, the option holder profits from the price difference. The lower the stock price goes below the strike price, the greater the payoff becomes. This is because the right to sell at a higher price becomes increasingly valuable as the market price falls further. This is the core benefit of holding a long put option: it allows investors to profit if a stock price declines, while their potential loss is limited to the premium they initially paid if the stock price stays at or above the strike price.