Put Options - The Basics

At expiry, if the underlying price is below the strike price of a put, the put option has a value equal to the distance between the strike price and the underlying price. The lower the price of the underlying, the more the option will be worth. Alternatively, if at expiry the underlying price is above the strike price of the put, the put option has a value of zero.

The put option can’t have a negative value at expiry, but it can have a potentially large positive value, which of course makes it an attractive position to hold. Naturally the trader on the other side who is selling the put is not going to give this attractive property away for free, so the buyer of a put option must pay a premium up front to the seller of the put.

All of this together results in a payoff chart that looks like the following.

This example shows a long put option position with the following properties:

• Strike price: $95

• Option Premium: $5

• Contracts: 1

• Contract multiplier: 100

Notice from the shape of the payoff, that the risk is fixed, because no matter how high the underlying price goes, the most that the put option buyer can lose is the premium they paid for the option. To the downside though, they still gain additional benefit from every further decrease in the underlying price. In other words, for a long put, the maximum loss is capped, but the maximum profit is only capped by the underlying price reaching zero*.

*Note: As happened to WTI oil prices in April 2020, it is possible for the price of some assets to go negative, meaning that zero would not be a boundary for price, or the resulting option payoffs. However, most assets have a logical boundary at zero.

As can be seen on the chart, if the underlying price is above the strike price of 95 at expiry, the losses are limited to the total premium paid of $500 (calculated as the premium of $5 multiplied by the contract multiplier of 100).

If the underlying price is below the strike price of 95 at expiry, the holder of the put option receives a payment equal to the difference between the strike price and the underlying price.

More generally, the profit of a put option position at expiry is given by the following formula.

Put_Option_Profit = (MAX(0, Strike - Price) - Premium) * Contracts * Contract_Multiplier

Where:

• MAX(A, B) gives the highest value of A and B.

• Strike is the strike price of the option.

• Price is the underlying price at expiry.

• Premium is the price paid for the option.

• Contracts is the position size, with short positions represented as negative values.

• Contract_Multiplier is the multiplier for the option (e.g. 100 for equity options)

So let’s say we were holding the above example put option position, and at expiry the underlying price was $80.

We would therefore have the following:

• Strike: 95

• Price: 80

• Premium: 5

• Contracts: 1

• Contract_Multiplier: 100

Resulting in a profit of:

Put_Option_Profit = (MAX(0, 95 - 80) - 5) * 1 * 100

Put_Option_Profit = 10 * 1 * 100

Put_Option_Profit = $1,000

If instead, the underlying price at expiry was $110, the profit would be calculated as follows:

Put_Option_Profit = (MAX(0, 95 - 110) - 5) * 1 * 100

Put_Option_Profit = -5 * 1 * 100

Put_Option_Profit = -$500

So a $500 loss, which is equal to the total premium that was initially paid for the option.

What if we had sold this same put instead of bought it? The payoff would then look like this:

The key thing to note here is that for a short put, the maximum profit is capped at the premium collected, but the maximum loss is only capped by the price reaching zero. And losses can be far greater than the premium that was collected for selling the put. For this reason, when selling options, it is extremely important to first be aware of the risks, and also to manage those risks.

We can still use the same formula to calculate the profit/loss, we just need to bear in mind that our position size should be entered as a negative number as we are now short the option.

Now let’s say we were holding the short put position, and at expiry the underlying price was $80.

We would therefore have the following:

• Strike: 95

• Price: 80

• Premium: 5

• Contracts: -1

• Contract_Multiplier: 100

Resulting in a profit of:

Put_Option_Profit = (MAX(0, Strike - Price) - Premium) * Contracts * Contract_Multiplier

Put_Option_Profit = (MAX(0, 95 - 80) - 5) * -1 * 100

Put_Option_Profit = 10 * -1 * 100

Put_Option_Profit = -$1,000

If instead, the underlying price at expiry was $110, the profit would be calculated as follows:

Put_Option_Profit = (MAX(0, 95 - 110) - 5) * -1 * 100

Put_Option_Profit = -5 * -1 * 100

Put_Option_Profit = $500

As we’ve seen with these examples, any gain for the buyer of a put represents a loss for the seller of that same put, and vice versa. The rights and obligations are also reversed, with the buyer having the right to sell the asset at the strike price, whereas the seller is obligated to buy the asset at the strike price. 

The most important difference to be aware of with regards to buying vs selling options, is the difference in risk. The buyer of a put option has a fixed risk because the most they can possibly lose is the premium they have paid for the option. However, the seller of the put option has risk that is only capped by the underlying price reaching zero (and there are even examples of negative asset prices), because they need to pay out an additional $1 for every $1 lower the underlying price is than the strike price at expiry.

Purely from a risk point of view then, being long put options is clearly superior, however the buyer of the option must pay a premium up front to the seller for their position. If held to expiry and the underlying price is not below the strike price, the seller gets to keep the entire premium. This premium is the seller’s compensation for taking on the riskier position.

In the above examples, we have only covered the profit/loss at the moment of expiry. When an option position is not held to expiry, but instead closed early, the profit and loss calculation is very simple. Every completed trade involves a buy order and a sell order, so you simply subtract what you bought the option for, from what you sold it for.

This is true for both American and European options because we’re talking here about closing a position by selling it to someone else, not about exercising the option.

To close an option position early:

• If you are long an option, closing the position would be done by selling the option to another trader, reducing your net position to zero.

• If you are short an option, closing the position would be done by buying the option from another trader, reducing your net position to zero.

Product availability varies by jurisdiction. Fees apply. Options trading carries significant risk and may not be suitable for everyone. Leverage in futures trading can work for you or against you. The risk of loss using leverage can exceed your initial investment amount. Information is provided for informational purposes only and is not investment advice. This is not a recommendation to buy or sell a particular digital asset or to employ a particular investment strategy.