# Archimedes Finance

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## Creating a map when selling options

Lesson in Course: Derivatives and options (expert, 6min )

I can understand and read the payoff diagrams when I buy call and put options. What about when I sell options? Selling option contracts is synonymous with shorting option contracts. We should become comfortable with using the descriptors "selling" and "shorting" interchangeably as most options traders already do. We already know that short call and put options expose us to additional risk compared to just buying calls and puts. The risk is harder to understand if we can't see it visually. Let's learn how to make sense of the pay-off diagrams for short calls and puts.

### KEY TAKEAWAYS:

The three takeaways for this lesson are:

• Know how to convert pay-off diagrams to short pay-off diagrams
• Understand how to visually interpret a short call diagram
• Understand how to visually interpret a short put diagram

Being able to recognize the pay-off diagrams of short option positions will help us begin to understand the ways we can make or lose money when selling options.

## The inverse relationship

Instead of starting from scratch, we can lean on the knowledge we've gained from understanding pay-off diagrams for buying options.

### options are considered zero-sum

Added together, the gains and losses between option holders and sellers equal 0.

Let's revisit the concept that an options contract represents an exchange of value between two different investors. Within this contract, for every single dollar in value received by one investor, the other is losing the same amount. Understanding this inverse relationship helps us to be able to construct payoff diagrams for selling options. To create payoff diagrams for selling options, we would simply just invert the purchase diagrams vertically.

Let's watch a quick video breaking the concept down.

## Understanding payoff diagrams for short positions

The value diagram for a short position is not very helpful since we aren't holders of the option. Value diagrams help us see the intrinsic value and as option writers, we don't get a choice to exercise the options. In reality, we are hoping the intrinsic value stays below \$0 so we can pocket the premiums.

For example, if we sold a \$50 strike call option on a stock for \$10 in premiums we can expect the profit diagram to look like the red-lined graph below.

We make money (the premium collected) as the seller until the stock is at \$60 (premium + strike), the break-even point for the call. After the break-even point, the call option is now in-the-money for the holder of the option and we face the risk of being assigned. Every additional dollar that the option moves in-the-money results in a dollar loss for us. We want the stock to stay below break-even when we short a call.

For a short put, the concept works very similarly.

Recall that break-even for a put is calculated differently and has to be lower than the strike price since a put option bets against the stock price. The put break-even is the strike value subtracted by the premium or \$40 in the example.

As the put writer, we make money by collecting the premium as long as the put option stays out-of-the-money, or above the break-even at \$40. If the stock price drops below \$40, we will have losses and be at risk of assignment.

An easy way to identify short profit diagrams when we see one is that they are short in height. For short calls and puts, the most we can stand to make is the premium collected for selling those options. The limited profit is what makes the graph short vertically short. The graph also shows us that shorting options can expose us to a lot of downside risk, or the risk to lose our money. In the diagrams above, while the maximum gains are capped, the losses can be great. We'll cover the risk profile of short option positions in more detail in future lessons.

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