# Put option payoff example

For example, if underlying price is You can immediately buy it back on the market for Above the strike, the put option has zero value, because there is no point exercising the right to sell the underlying at strike price when you can sell it for a higher price without the option. The first component is equal to the difference between strike price and underlying price.

The lower underlying price gets relative to strike price, the higher your cash gain at expiration. However, this only applies when underlying price is below strike price. When it gets above, the result would be negative you would be losing money by exercising the option. Because a put option gives you the right but not obligation to sell, if underlying price is above strike price, you choose to not exercise the option and therefore cash flow at expiration is zero.

Taking all scenarios into consideration, a long put option cash flow at expiration is therefore the higher of:. The above is per share. To get the total dollar amount, you need to multiply it by number of contracts and contract multiplier number of shares per contract. Initial cost is of course the same under all scenarios. Therefore the formula for long put option payoff is:.

It is very easy to calculate the payoff in Excel. The key part is the MAX function; the rest is basic arithmetics. You can see all the formulas in the screenshot below. A call option gives you the right, but not obligation, to buy the underlying security at the given strike price.

Below the strike, the payoff chart is constant and negative the trade is a loss. For example, if underlying price is Same as scenario 1 in fact. Finally, this is the scenario which a call option holder is hoping for.

Because the option gives you the right to buy the underlying at strike price If you bought the option at 2. You can also see this in the payoff diagram where underlying price X-axis is Initial cash flow is constant — the same under all scenarios.

It is a product of three things:. Of course, with a long call position the initial cash flow is negative, as you are buying the options in the beginning.

The second component of a call option payoff, cash flow at expiration, varies depending on underlying price. That said, it is actually quite simple and you can construct it from the scenarios discussed above. If underlying price is below than or equal to strike price, the cash flow at expiration is always zero, as you just let the option expire and do nothing. If underlying price is above the strike price, you exercise the option and you can immediately sell it on the market at the current underlying price.

The put writer's total potential loss is limited to the put's strike price less the spot and premium already received. Puts can be used also to limit the writer's portfolio risk and may be part of an option spread. That is, the buyer wants the value of the put option to increase by a decline in the price of the underlying asset below the strike price.

The writer seller of a put is long on the underlying asset and short on the put option itself. That is, the seller wants the option to become worthless by an increase in the price of the underlying asset above the strike price.

Generally, a put option that is purchased is referred to as a long put and a put option that is sold is referred to as a short put. A naked put , also called an uncovered put , is a put option whose writer the seller does not have a position in the underlying stock or other instrument.

This strategy is best used by investors who want to accumulate a position in the underlying stock, but only if the price is low enough. If the buyer fails to exercise the options, then the writer keeps the option premium as a "gift" for playing the game. If the underlying stock's market price is below the option's strike price when expiration arrives, the option owner buyer can exercise the put option, forcing the writer to buy the underlying stock at the strike price.

That allows the exerciser buyer to profit from the difference between the stock's market price and the option's strike price. But if the stock's market price is above the option's strike price at the end of expiration day, the option expires worthless, and the owner's loss is limited to the premium fee paid for it the writer's profit.

The seller's potential loss on a naked put can be substantial. If the stock falls all the way to zero bankruptcy , his loss is equal to the strike price at which he must buy the stock to cover the option minus the premium received. The potential upside is the premium received when selling the option: During the option's lifetime, if the stock moves lower, the option's premium may increase depending on how far the stock falls and how much time passes. If it does, it becomes more costly to close the position repurchase the put, sold earlier , resulting in a loss.

If the stock price completely collapses before the put position is closed, the put writer potentially can face catastrophic loss. In order to protect the put buyer from default, the put writer is required to post margin. The put buyer does not need to post margin because the buyer would not exercise the option if it had a negative payoff. A buyer thinks the price of a stock will decrease.