Introduction to payout diagrams of call and put options
Hi there. This is Sushant Reddy from BigBlind series on options trading. In this tutorial, I introduce payout diagrams for options. Payout diagrams are a good way of visualizing your profitability in different scenarios. Payout diagrams are even more helpful when you are looking at option strategies that involve multiple options.
What is a payout diagram
Payout diagrams plots the profit/loss of an option against stock price. P/L is plotted on y-axis and stock price is plotted on x-axis. Another important dimension is ‘time’ — payout is captured at a specific time. In this tutorial we always assume that this time is day of expiry.
Call option buyer
A quick recap — a call option buyer has a right but not an obligation to buy the stock at ‘strike price’ on expiry date,
Let’s look at payout of a call option buyer on the day of expiry. Two important points marked on x and y-axis are the ‘strike price’ and ‘premium’. As discussed in previous tutorial, call option has a payout if stock price is greater than strike price & ‘premium’ is amount paid upfront by option holder to buy the option.
So payout of call option buyer at expiry looks something like this:
When stock price < strike price, call option has zero payout at expiry. Since an option buyer has purchased the instrument by paying upfront premium, overall P/L in this case is negative and loss is the premium paid upfront.
Maximum loss for call option buyer is equal to premium paid upfront.
When stock price > strike price, call option payout at expiry equals difference between stock price and strike price. P/L in this case is this payout at expiry minus the premium paid upfront. Since stock price can increase without any limit, there is no upside for payout of a call option.
Call option buyer theoretically can have an unlimited upside
Call option seller (writer)
For a call option seller, scenario is exactly opposite. A call option seller receives premium upfront and will have zero payout at expiry if stock price is less than strike price (case when buyer’s call option expires worthless). Similarly, when stock price is above strike price, a call option seller has to pay a difference of stock price and strike price.
Call option seller has a limited upside (upfront premium) and a theoretically unlimited downside
Here is payout and P/L equation for call option buyer and seller:
Put option buyer
A put option buyer has a right but not obligation to sell stock at strike price on expiry date.
So payout of put option buyer at expiry looks something like this:
A put option pays out if stock price on expiry date is less than strike price. Since a put option buyer will sell stock only when strike price is higher than stock price on that day, put option payout will be difference between strike price and stock price , if stock price is less than strike price, and zero otherwise.
Put option seller
A put option seller will receive an upfront premium and will have to pay if stock price on expiry date is less than strike price. If stock price on expiry is greater than stock price, a put option seller will retain the entire premium and make no payout.
Below are the payout and profitability equations for put option buyer and seller:
Asymmetric payout of options
One thing you must have noticed from these payout diagrams is that option instruments have asymmetric payouts — capped downside and unlimited upside (for buyer) and capped upside and unlimited downside (for seller).
We will look at this property in greater detail when we understand concepts of volatility and option greeks in future tutorials.
To summarize, in this tutorial, we looked at payouts diagrams and profitability for call and put options. I hope you found it useful — please leave your comments and feedback in section below.
