## Options Pricing: Profit and Loss Diagrams

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If you have seen the page explaining call option payoffyou will find the overall logic is very similar with puts; there are just a few differences which we will point out. While a call option gives you the right to buy the underlying security, a put option represents the right but not obligation to sell the underlying at the given strike price.

When holding a put option, you want the underlying price go down, because the lower it gets relative to the strike price, the more valuable your put option becomes. A long put option position is therefore a bearish trade — makes money when underlying price goes down and loses when it goes up.

You can see the payoff graph below. Of course, it also depends on your position size 1 contract representing shares in this example.

The relationships is linear and the slope depends on position long call option payoff formula. 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 long call option payoff formula 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 long call option payoff formula 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 long call option payoff formula by number of contracts and contract multiplier number of shares per contract.

Initial long call option payoff formula 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. Besides the strike price, another important point on the payoff diagram is the break-even point, which is the underlying price where the position turns from losing to profitable or vice-versa. Calculating the exact break-even price is very useful when evaluating potential option trades.

The formula for put option break-even point is actually very simple:. If you don't agree with any part of this Agreement, please leave the website now. All information is for educational purposes only and may be inaccurate, incomplete, outdated or plain wrong. Macroption is not liable for any damages resulting from using the content. No financial, investment or trading advice is given at any time.

Home Calculators Tutorials About Contact. Tutorial 1 Tutorial 2 Tutorial 3 Tutorial 4. Put Option Payoff Diagram and Formula. This page explains put option payoff. We will look at: Long Put Option Position is Bearish While a long call option payoff formula option gives you the right to long call option payoff formula the underlying security, a put option represents the right but not obligation to sell the underlying at the given strike price.

Put Option Payoff Diagram You can see the payoff graph below. Put Option Scenarios and Profit or Loss 1. What you can get when exercising the option What you have paid for the option in the beginning The first component is equal to the difference between strike price and underlying price.

Taking all scenarios into consideration, a long put option cash flow at expiration is therefore the higher of: Therefore the long call option payoff formula for long put option payoff is: Put Option Break-Even Point Calculation Besides the strike price, another important point on the long call option payoff formula diagram is the break-even point, which is the underlying price where the position turns from losing to profitable or vice-versa.

The formula for put option break-even point is actually very simple: Long Put Option Payoff Summary A long put option position is bearish, with limited risk and limited but usually very high potential profit.

Maximum possible loss is equal to initial cost of the option and applies for underlying price higher than or equal to the strike price. With underlying price long call option payoff formula the strike, the payoff rises in proportion with underlying price. The position turns profitable at break-even underlying price equal to strike price minus initial option price.

Maximum theoretical profit which would apply if the underlying price dropped to zero is per share equal to the break-even price.

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Here you can see the same for put option payoff. And here the same for short call position the inverse of long call. Buying a call option is the simplest of option trades. 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.

Therefore the cash flow is the difference between underlying price and strike price, times number of shares. Putting all the scenarios together, we can say that the cash flow at expiration is equal to the greater of:. It is the same formula. The screenshot below illustrates call option payoff calculation in Excel. Besides the MAX function, which is very simple, it is all basic arithmetics. One other thing you may want to calculate is the exact underlying price where your long call position starts to be profitable.

If you don't agree with any part of this Agreement, please leave the website now. All information is for educational purposes only and may be inaccurate, incomplete, outdated or plain wrong.

Macroption is not liable for any damages resulting from using the content. No financial, investment or trading advice is given at any time. Home Calculators Tutorials About Contact.

Tutorial 1 Tutorial 2 Tutorial 3 Tutorial 4. We will look at: Call Option Payoff Diagram Buying a call option is the simplest of option trades. The key variables are: Strike price 45 in the example above Initial price at which you have bought the option 2. Call Option Scenarios and Profit or Loss Three things can generally happen when you are long a call option. Underlying price is higher than strike price Finally, this is the scenario which a call option holder is hoping for.

Call Option Payoff Formula The total profit or loss from a long call trade is always a sum of two things: Initial cash flow Cash flow at expiration Initial cash flow Initial cash flow is constant — the same under all scenarios. It is a product of three things: Cash flow at expiration The second component of a call option payoff, cash flow at expiration, varies depending on underlying price. Call Option Break-Even Point Calculation One other thing you may want to calculate is the exact underlying price where your long call position starts to be profitable.

It is very simple. It is the sum of strike price and initial option price. Long Call Option Payoff Summary A long call option position is bullish, with limited risk and unlimited upside. Maximum possible loss is equal to initial cost of the option and applies for underlying price below than or equal to the strike price.

With underlying price above the strike, the payoff rises in proportion with underlying price. The position turns profitable at break-even underlying price equal to the sum of strike price and initial option price.