Moneyness At Expiration

What Moneyness Means at Expiration

At expiration, an option’s moneyness describes the position of the underlying asset’s market price relative to the option’s exercise price, also called its strike. The comparison tells whether exercising the option would produce a positive payoff. It does not, by itself, tell whether the option position earned a profit: the premium paid or received also matters.

Let $S_T$ be the underlying asset’s price at expiration and $K$ the option’s exercise price. The classification applies to the contract, whether a trader is long or short that contract. A long position owns the exercise right; a short position has the corresponding obligation if the option is exercised. Neither position changes the relationship between $S_T$ and $K$.

Definition: At expiration, a call is in the money if $S_T>K$, at the money if $S_T=K$, and out of the money if $S_T<K$. A put is in the money if $S_T<K$, at the money if $S_T=K$, and out of the money if $S_T>K$.

The direction reverses for a put because the call holder has the right to buy at $K$, while the put holder has the right to sell at $K$. A call benefits from a market price above its strike; a put benefits from a market price below its strike. At equality, neither right produces a positive payoff through exercise.

Why the Classification Matches the Payoff

Assume a standard option on one unit of an underlying asset, with no additional contractual adjustment to the exercise price. Write $z^+=\max(z,0)$. The expiration payoffs to the long call and long put are:

C_T=(S_T-K)^+,\qquad P_T=(K-S_T)^+.

These formulas follow directly from the exercise choices. Exercising a call means paying $K$ for an asset worth $S_T$, so the net amount from exercise is $S_T-K$. The holder can instead decline to exercise, receiving zero from the option at expiration. The payoff is therefore the greater of $S_T-K$ and zero. Exercising a put means delivering an asset worth $S_T$ in exchange for $K$, producing $K-S_T$; again, the holder can decline and receive zero. This gives the put formula.

The sign of the expression inside each maximum establishes the classification. For a call, $S_T-K$ is positive exactly when $S_T>K$. For a put, $K-S_T$ is positive exactly when $S_T<K$. If $S_T=K$, each expression is zero. This is why “in the money” corresponds to a positive exercise payoff, while “at the money” and “out of the money” both have zero payoff at expiration.

Key result: At expiration, an in-the-money option has a positive exercise payoff. An at-the-money or out-of-the-money option has a zero exercise payoff. The at-the-money case is the precise equality $S_T=K$, not a range of prices.

A Reliable Classification Method

For each option, first identify its own strike and the expiration price of its underlying asset. Then compare those two amounts. Do not classify by whether the price rose or fell from the date the option was purchased, and do not use the premium as a substitute for the strike.

Read the contract.
Record whether it is a call or put and identify the strike $K$ and expiration price $S_T$.

Compare price and strike.
For a call, check whether $S_T$ is greater than, equal to, or less than $K$. For a put, use the reversed comparison.

Check with the payoff.
Evaluate $(S_T-K)^+$ for a call or $(K-S_T)^+$ for a put. A positive amount confirms that the option is in the money; zero is consistent with either at the money or out of the money.

Keep profit separate.
If asked for profit, account for the premium and the stated treatment of that premium. Do not let the profit result change the moneyness classification.

Worked Example: Comparing a Call and Put at the Same Strike

A hypothetical stock option pair has a common strike of $K=\$50.00$. At expiration, the stock price is $S_T=\$47.50$. The long call’s premium was $\$1.20$ per share and the long put’s premium was $\$2.10$ per share. Classify each option and calculate each long position’s expiration payoff and simple profit per share. Ignore financing, taxes, and transaction costs; measure simple profit as expiration payoff minus premium paid.

Method. Compare the expiration price with the common strike, then apply the payoff formulas. The premium is used only after classification, when calculating profit.

Call. Since $\$47.50<\$50.00$, the call is out of the money. Its payoff is $C_T=\max(\$47.50-\$50.00,0)=\max(-\$2.50,0)=\$0.00$. Its simple profit is $\$0.00-\$1.20=-\$1.20$ per share.

Put. Since $\$47.50<\$50.00$, the put is in the money. Its payoff is $P_T=\max(\$50.00-\$47.50,0)=\max(\$2.50,0)=\$2.50$. Its simple profit is $\$2.50-\$2.10=\$0.40$ per share.

Check. Only the put has a positive exercise payoff, as expected when the market price is below the strike. The call’s zero payoff does not prevent it from having a loss: the premium paid remains a cost. The put is in the money and has a positive profit here, but those facts are not equivalent in general.

Moneyness Is Not Profitability

Moneyness is determined by $S_T$, $K$, and whether the contract is a call or a put. It does not depend on the premium, the date of purchase, or whether the position is long or short. Profit, in contrast, compares the payoff with the cash flows associated with entering the position. For a simple, undiscounted calculation, a long option’s profit is payoff minus premium paid; a short option’s profit is premium received minus the amount paid to the long holder. If a problem specifies a different timing or financing convention, use that convention for profit while keeping the moneyness test unchanged.

An option may be in the money but still have a negative simple profit if its premium exceeds its payoff. An option that is out of the money at expiration has zero exercise payoff, but a long holder who paid a premium has a loss under the simple profit convention. A short holder’s profit also does not determine the contract’s moneyness.

Worked Example: An In-the-Money Call Can Still Lose Money

A hypothetical call has strike $K=\$72.00$, and the underlying asset expires at $S_T=\$76.00$. A trader bought the call for a premium of $\$5.25$ per share. Classify it, calculate its expiration payoff, and find the trader’s simple profit per share. Ignore financing, taxes, and transaction costs.

Method. Determine moneyness from the price-strike comparison before considering the premium.

Because $\$76.00>\$72.00$, the call is in the money. Its payoff is $C_T=\max(\$76.00-\$72.00,0)=\$4.00$ per share.

The simple profit is payoff minus premium: $\$4.00-\$5.25=-\$1.25$ per share. Thus the call is in the money but the long position has a simple loss of $\$1.25$ per share.

Check. Exercising creates a $\$4.00$ payoff, which is positive and confirms the in-the-money classification. The initial $\$5.25$ premium is larger than that payoff, explaining the loss. The mistake to avoid is calling the option out of the money merely because the trader lost money.

The Equality Case and Position Direction

At $S_T=K$, both the call and the put are at the money. The call holder could buy for $K$ an asset worth exactly $K$, and the put holder could sell an asset worth $K$ for exactly $K$. Either exercise yields zero before considering any other cash flows. The equality case is worth checking explicitly: an option with zero payoff is not automatically out of the money, because an at-the-money option also has zero payoff.

The same contract has the same moneyness for its long and short positions. A short call does not become out of the money when $S_T>K$; the call contract is in the money, and the short position has the corresponding payment obligation if exercised. Position direction changes the sign of the holder’s and writer’s cash flows, not the comparison used to classify the option.

Worked Example: Classifying Several Positions at Expiration

At expiration, a hypothetical asset is priced at $S_T=\$84.00$. Consider (1) a long call with strike $\$80.00$, premium paid $\$3.00$; (2) a long put with strike $\$90.00$, premium paid $\$8.00$; and (3) a short call with strike $\$84.00$, premium received $\$2.00$. For each, state the contract’s moneyness, the position’s payoff, and its simple profit per share. Ignore financing, taxes, and transaction costs.

Method. Classify each contract using its own strike, then calculate the long holder’s payoff. A short position has the opposite option payoff; its simple profit is the premium received minus the amount paid to the holder.

(1) Long call, $K=\$80.00$. Since $\$84.00>\$80.00$, the call is in the money. The long payoff is $\max(\$84.00-\$80.00,0)=\$4.00$. Simple profit is $\$4.00-\$3.00=\$1.00$ per share.

(2) Long put, $K=\$90.00$. Since $\$84.00<\$90.00$, the put is in the money. The long payoff is $\max(\$90.00-\$84.00,0)=\$6.00$. Simple profit is $\$6.00-\$8.00=-\$2.00$ per share.

(3) Short call, $K=\$84.00$. Since $S_T=K$, the call contract is at the money. Its long-holder payoff is $\max(\$84.00-\$84.00,0)=\$0.00$, so the short position’s option payoff is also $\$0.00$. The short seller retains the $\$2.00$ premium, giving simple profit of $\$2.00-\$0.00=\$2.00$ per share.

Check. The first two contracts are in the money because their respective exercise payoffs are positive. The third is exactly at the money, not out of the money. Its profit is positive because of the premium, but the premium does not change that classification.

Common Classification Errors

Using one rule for both option types. A higher expiration price helps a call’s moneyness but makes a put out of the money. Reverse the inequality for puts.
Confusing zero payoff with out of the money. Both at-the-money and out-of-the-money options have zero payoff at expiration. Compare $S_T$ and $K$ to distinguish them.
Classifying from profit or premium. A premium may make an in-the-money position unprofitable, but moneyness still follows only from the contract type and price-strike comparison.
Ignoring which strike belongs to which contract. In a set of options, compare the expiration price with each option’s own strike, not with another option’s strike.
Changing classification for a short position. Long and short positions in the same contract share the same moneyness. Their payoffs have opposite signs.

A quick final check is to calculate the applicable expiration payoff. A positive call payoff requires $S_T>K$; a positive put payoff requires $S_T<K$. If the payoff is zero, check whether the prices are equal before labeling the option out of the money.

Check Your Understanding

For each problem, classify the specified option at expiration. Where requested, calculate payoff and simple profit using the stated convention. Ignore financing, taxes, and transaction costs unless specified otherwise.

A call has strike $\$46.00$, the asset expires at $\$46.00$, and the long holder paid a $\$1.35$ premium. State its moneyness, payoff, and simple profit per share. (Answer: At the money; payoff $\$0.00$; simple profit $-\$1.35$ per share.)
A put has strike $\$118.00$, and the underlying expires at $\$111.00$. The long holder paid $\$8.25$. State moneyness, payoff, and simple profit per share. (Answer: In the money; payoff $\$7.00$; simple profit $-\$1.25$ per share.)
An asset expires at $\$39.00$. A trader holds a short call with strike $\$42.00$, for which the trader received a $\$1.10$ premium. State the contract’s moneyness, the short position’s option payoff, and its simple profit per share. (Answer: Out of the money; short option payoff $\$0.00$; simple profit $\$1.10$ per share.)
An asset expires at $\$155.00$. A long call has strike $\$150.00$ and premium $\$6.40$; a long put has strike $\$160.00$ and premium $\$3.50$. Classify both and calculate each simple profit per share. (Answer: The call is in the money with payoff $\$5.00$ and profit $-\$1.40$; the put is in the money with payoff $\$5.00$ and profit $\$1.50$.)
An asset expires at $\$73.00$. A short call has strike $\$70.00$ and premium received $\$4.20$; a short put has strike $\$76.00$ and premium received $\$2.10$. For each contract, state moneyness, the short position’s option payoff, and simple profit per share. (Answer: The call is in the money; short option payoff $-\$3.00$, profit $\$1.20$. The put is in the money; short option payoff $-\$3.00$, profit $-\$0.90$.)

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