What is the payout of an option?

The payout of an option refers to the net profit or loss realized by the option holder at the option's expiration, calculated by subtracting the initial premium paid from the option's intrinsic value, if any. This calculation determines the financial outcome for the investor holding the option contract.

Understanding Option Payout

An option contract gives the holder the right, but not the obligation, to buy or sell an underlying asset at a predetermined price (the strike price) on or before a specific date. The "payout" at expiration depends on the relationship between the underlying asset's price and the option's strike price, as well as the initial cost (premium) paid to acquire the option.

Key factors determining an option's payout include:

• Underlying Asset Price: The market price of the stock or other asset at the option's expiration.
• Strike Price: The fixed price at which the option holder can buy (for a call) or sell (for a put) the underlying asset.
• Premium Per Share: The upfront cost paid by the option holder to acquire the contract. This is a crucial component in calculating the net payout.

Calculating Payout for Long Call Options

A long call option is purchased by an investor who expects the underlying asset's price to rise. The holder of a call option profits if the stock price at expiration is above the strike price.

The payout for a long call option per share is calculated using the following formula:

Call Payout Per Share = (MAX (Stock Price - Strike Price, 0) - Premium Per Share)

Let's break down this formula:

• Stock Price - Strike Price: This calculates the difference between the stock's price at expiration and the strike price.
• MAX (..., 0): This function ensures that the intrinsic value is never negative. If the stock price is below the strike price, the call option would not be exercised, and its intrinsic value is considered zero. This limits the potential loss for the option holder to only the premium paid.
• Premium Per Share: The cost initially paid for each share covered by the option. This is subtracted because it's a sunk cost that reduces any potential profit or adds to the loss.

Example: Long Call Option Payout

Suppose you buy a call option with a strike price of $100 and pay a premium of $5 per share.

• Scenario 1: Stock price at expiration is $110
  • Intrinsic Value = MAX ($110 - $100, 0) = MAX ($10, 0) = $10
  • Call Payout = $10 - $5 = $5 per share (a profit)
• Scenario 2: Stock price at expiration is $105
  • Intrinsic Value = MAX ($105 - $100, 0) = MAX ($5, 0) = $5
  • Call Payout = $5 - $5 = $0 per share (break-even point)
• Scenario 3: Stock price at expiration is $95
  • Intrinsic Value = MAX ($95 - $100, 0) = MAX (-$5, 0) = $0
  • Call Payout = $0 - $5 = -$5 per share (a loss, limited to the premium paid)

The break-even point for a long call option is the strike price plus the premium paid. In the example above, $100 (strike) + $5 (premium) = $105.

Calculating Payout for Long Put Options

A long put option is purchased by an investor who expects the underlying asset's price to fall. The holder of a put option profits if the stock price at expiration is below the strike price.

The payout for a long put option per share is calculated using the following formula:

Put Payout Per Share = (MAX (Strike Price - Stock Price, 0) - Premium Per Share)

Let's break down this formula:

• Strike Price - Stock Price: This calculates the difference between the strike price and the stock's price at expiration.
• MAX (..., 0): This function ensures the intrinsic value is never negative. If the stock price is above the strike price, the put option would not be exercised, and its intrinsic value is considered zero. This limits the potential loss for the option holder to only the premium paid.
• Premium Per Share: The cost initially paid for each share covered by the option. This is subtracted because it's a sunk cost that reduces any potential profit or adds to the loss.

Example: Long Put Option Payout

Suppose you buy a put option with a strike price of $100 and pay a premium of $5 per share.

• Scenario 1: Stock price at expiration is $90
  • Intrinsic Value = MAX ($100 - $90, 0) = MAX ($10, 0) = $10
  • Put Payout = $10 - $5 = $5 per share (a profit)
• Scenario 2: Stock price at expiration is $95
  • Intrinsic Value = MAX ($100 - $95, 0) = MAX ($5, 0) = $5
  • Put Payout = $5 - $5 = $0 per share (break-even point)
• Scenario 3: Stock price at expiration is $105
  • Intrinsic Value = MAX ($100 - $105, 0) = MAX (-$5, 0) = $0
  • Put Payout = $0 - $5 = -$5 per share (a loss, limited to the premium paid)

The break-even point for a long put option is the strike price minus the premium paid. In the example above, $100 (strike) - $5 (premium) = $95.

Why the "MAX (X, 0)" is Crucial

The MAX (X, 0) component in both payout formulas is fundamental to understanding options. It represents the "optionality" of the contract. Since an option holder is not obligated to exercise the option, they will only do so if it is financially advantageous (i.e., if exercising yields a positive intrinsic value). If exercising would result in a loss (e.g., buying stock at $100 when it's trading at $90 with a call, or selling stock at $100 when it's trading at $110 with a put), the option holder simply lets the option expire worthless. In such cases, the gross payout (before subtracting premium) is zero, and the net payout is simply the negative of the premium paid.

Payout Scenarios Overview

The table below summarizes the payout for both long call and long put options based on the stock price relative to the strike price at expiration.

Understanding these payout calculations is essential for investors to assess the potential profitability and risk associated with buying call and put options.