Pay-off Diagrams for Option

Pay-off diagrams can be used as a means of illustrating the risk/return profile of an option position. Pay-off diagrams allow you to visualize any trading strategy in a static form.

The x-axis (horizontal line) of a pay-off diagram represents the price of the underlying asset
The y-axis (vertical line) of a pay-off diagram represents the profit/loss on the option position.

Pay-off Diagrams for Options

There are four basic pay-off diagrams for options:

The Option Buyer

1. Long Call

Pay-off diagram below represents the effective pay-off of a long call position of an option at the time of the expiry date. It looks at the option from the point of view of buyer.

If a trader believes the share of a company is on the rise, he can purchase a call option without buying the share. Assume he bought a call option (strike price is $5 and premium is 50 cent). The break even point for this trade is $5.50. If at expiry date, the underlying share is trading at a point between $5 and $5.50, he will be able to recover portion of the premium by exercising the option. If the share is above $5.50 at this time, there will be a linear relationship between the share price and the profit. If the share price has moved up to $6 by the option expiry date, the profit on the option will be $0.50 (the different between the exercise price, which is $5, and the current share price, less the option premium, which is $0.50)

2. Long Put

Pay-off diagram below represents the effective pay-off of a long put position of an option at the time of the expiry date. It looks at the option from the point of view of buyer.

If a trader believes the share of a company is on the decline, he can make money by buying put options. Assume he bought a long option (strike price is $5 and premium is 50 cent). Two week later, the share price falls to $4.5. The put option now has intrinsic value of $0.50. It will also have a time value, likely to be $0.30. The option can now be sold in the marketplace for a premium value of $0.80. The profit would be $0.30.

If at expiry date, the underlying share is traded at or above $5, there will be a loss of the full premium. The break even point for this option is $4.50, which is equal to the strike price minus the premium. If the share is trading below $4.50 by option expiry date, the option buyer would make a profit. There will be a linear relationship between the share price and the option profit.

The Option Seller

3. Short Call

Option seller has limited profit potential and potentially unlimited risk. Pay-off diagram below represents the effective pay-off of a short call position of an option at the time of the expiry date. It looks at the option from the point of view of seller.

Diagram below shows a call option with a premium of 50 points. This position is the reverse of the buyer’s. If the share price is below $5 at the expiry date, the seller will earn the full premium 50 point, which is $0.50. This is the most he can earn. The break even point for this option is the same as the buyer, which is $5.50. At this price, the premium earned will be exactly offset by the losses on the option position. If the share price moves above $5.50, the option seller’s loss moves in a linear relationship with the share price. At $6, the option seller’s loss will be $0.50 (made up of $1 loss on the option position less the premium earned of $0.50).

4. Short Put

Pay-off diagram below shows the effective pay-off of a short put position of an option at the time of the expiry date. It looks at the option from the point of view of seller.

In this example, the seller will receive full premium if the share price is at or above $5 strike price. However if the share price drops, there is a linear relationship between the index and the loss made on this position. The break even point is $4.50, where the profit is equal to the loss incurred.

Pay-off Diagrams for the Underlying

Example 1: Long Stock:

Pay-off diagram below represents the pay-off of a long position in the cash market. Assume you purchase an ABC Co. share at $5. You are long stock. If the price of the stock remains at $5, there is no profit or loss. If the price increases to $5.25, you earn $0.25 in profit. However if the price drops to $4.75, your loss will be $0.25.

Example 2: Short Stock:

Pay-off diagram below represents the pay-off of a short position in the cash market. Assume you purchase an ABC Co. share at $5. You are now short the market. If the price of the stock drops to $4.75, you earn a profit of $0.25. However, if the price of the stock rises to $5.25, you make a loss of $0.25.

Related posts:

• Basic Option Strategies
• Option Strategies – Spreads
• Option Strategies – Straddles
• Option Strategies – Strangles