## Call Option Payoff Diagram, Formula and Logic

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There are two types of options - calls and puts. Also, for constructing these payoff diagrams I have ignored option premiums so we can focus on the payout. Option premiums can be considered constants that move the entire graph up or down, without changing its shape which is what we are interested in.

The payoff for a stock position is linear. The payoff increases or decreases short call option payoff graph with price, depending upon whether it is a long or a short position. A long position in a call option has a zero pay off till the exercise price, after which its payoff is identical to that of the stock.

Here is a simple trick that some may find useful to remember what option payoff diagrams look like. The one pay-off diagram you will need to remember is the long call.

Recall that this looks as follows:. To get the short call pay-off diagram, assume there is an imaginary mirror placed on the x-axis. This applies to every option position, or complex set of positions. To get the long put position from the long call, imagine there is a mirror along the y-axis this time. You get the pay-off from a long put position. Given this, you can visualize the payoff from a short put position too. Complex options positions can be understood by combining payoff diagrams.

Next, we will combine payoff diagrams to understand the put-call parity. Imagine an options portfolio with a long call and a short put position, both with the same exercise price. This will have the following payoff:. Compare the resulting payoff — the diagram on the right hand side. This looks just like the payoff for the stock, except that the line is a bit lower. And it is lower by exactly the amount of the exercise price, present valued to today.

Short call option payoff graph combining a long call with a short put, we end up short call option payoff graph a linear payoff, just like for the stock. This linear payoff, combined with a bank deposit, has a payoff identical to a stock:. This is the put-call parity. Notice the right hand side of this equation. The exercise price is a constant, and so is the spot price. So at any point in time, RHS is fixed. Therefore if call prices rise, put prices would rise need to rise too in order to maintain the parity.

The minus sign indicates a short position. Payoff for a stock position The payoff for a stock position is linear. The payoff short call option payoff graph a short stock position is just the opposite: The payoffs for a short call, a long put and a short put are given below: How to remember what different payoff diagrams look like: Recall that this looks as follows: Combining payoffs Complex options positions can be understood by combining payoff diagrams.

Understanding put-call parity Imagine an options portfolio with a long call and a short put position, both with the same exercise price. This will have the following payoff: This linear payoff, combined with a bank deposit, has short call option payoff graph payoff identical to a stock: Combining the two, we get: This can also be written as: So we can write the put call parity as: Introduction to vanilla options.

Payoff diagrams There are two types of options - calls and puts.

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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.