FRM Exam Part I · Properties of Options

Option Basics and Payoff Profiles for FRM Part 1

Q: What is the difference between option payoff and option profit?

Payoff is the cash value of the option at expiration, before considering what you paid for it. Profit is payoff minus the premium paid for a long position. For a writer, profit is the premium received minus the payoff made to the holder.

Q: What is the difference between intrinsic value and time value?

Intrinsic value is the amount the option would pay if exercised now: max(S − K, 0) for a call and max(K − S, 0) for a put. Time value is the premium minus intrinsic value. It reflects the chance that the option moves further into the money before expiry, and it is zero at expiration.

Q: How do I tell if an option is in the money, at the money or out of the money?

Compare the current asset price S with the strike K. A call is ITM when S > K and OTM when S K. Both are ATM when S = K.

Updated 11 October 2026 · Fact-checked

An option gives the holder the right, not the obligation, to buy (call) or sell (put) an asset at the strike price. At expiration, a long call pays max(S − K, 0) and a long put pays max(K − S, 0). Profit is payoff minus the premium paid. Short positions are the mirror image.

Understand Option Basics and Payoff Profiles

An option is a contract. The buyer (long) pays a premium to the seller (short, or writer). In return the buyer gets a right. A call gives the right to buy the underlying at the strike price K. A put gives the right to sell at K. A European option can be exercised only at expiration. An American option can be exercised any time up to expiration.

The buyer will exercise only if it helps. So the payoff can never be negative for the buyer. A call is worth exercising when the asset price S is above K. A put is worth exercising when S is below K. Otherwise the option expires worthless. The seller has the opposite position. The seller can never gain more than the premium received, and may owe a lot.

Moneyness describes the option's position relative to the strike. A call is in the money (ITM) if S > K, at the money (ATM) if S = K, and out of the money (OTM) if S < K. For a put, reverse it: ITM if S < K, OTM if S > K. Moneyness uses the current price, not the price paid for the option.

Option value has two parts. Intrinsic value is what you would get if you exercised now: max(S − K, 0) for a call, max(K − S, 0) for a put. Time value is the premium minus intrinsic value. An OTM option has zero intrinsic value, so its whole premium is time value. Time value reflects the chance of a better outcome before expiry, and it falls to zero at expiration.

Payoff ignores the premium. Profit includes it. Long positions have limited loss (the premium) and the long call has unlimited upside. The short call has limited gain (the premium) and unlimited loss. The long put has a maximum payoff of K (when S falls to 0). Long and short positions are zero-sum: the writer's payoff is exactly the negative of the holder's.

Key formulas to remember

Long call payoff: max(S_T − K, 0); S_T is the underlying price at expiration. Never negative.
Long put payoff: max(K − S_T, 0); Maximum possible payoff is K, when S_T = 0.
Short call payoff: −max(S_T − K, 0) = min(K − S_T, 0); Never positive. Loss is unlimited.
Short put payoff: −max(K − S_T, 0) = min(S_T − K, 0); Never positive. Worst payoff is −K (when S_T = 0). Worst profit is −(K − premium received).
Profit for long position: Profit = Payoff − Premium paid; Ignores time value of money unless the question says to compound the premium.
Profit for short position: Profit = Premium received − Buyer's payoff; Equals the negative of the long position's profit.
Breakeven price: Call: S_T = K + premium. Put: S_T = K − premium; Same breakeven for long and short in the same option.
Intrinsic value and time value: Call intrinsic = max(S − K, 0). Put intrinsic = max(K − S, 0). Time value = Premium − Intrinsic value; Time value of an option before expiry is normally not negative for the options in this topic.

How to solve Option Basics and Payoff Profiles questions

Use the same sequence for any payoff or profit question. It keeps signs correct for short positions.

1Identify the option type (call or put) and your side (long or short).
2Write down K, the premium, and the underlying price at expiration (or today, for moneyness).
3Compute the holder's payoff: max(S − K, 0) for a call or max(K − S, 0) for a put.
4If you are short, change the sign of that payoff.
5Adjust for the premium: subtract it if long, add it if short, to get profit.
6If asked for breakeven, set profit to zero: K + premium for a call, K − premium for a put.
7For moneyness or time value, compare S with K for the option type, then use Premium − Intrinsic value.
8Check the answer: a long position's loss cannot exceed the premium, and the long and short results must sum to zero.

Quickest way: Holder first, then flip the sign

When to use it: Use for any expiration payoff or profit question with a single option, especially when time is short.

Ask only: is the option ITM at expiration? If not, the holder's payoff is 0 and the long profit is −premium.
If ITM, payoff is the distance S − K (call) or K − S (put).
Long profit = payoff − premium. Short profit = −(long profit).
Breakeven: K + premium for a call, K − premium for a put.
Eliminate options that show a long loss larger than the premium or a short gain larger than the premium.

Common mistakes in Option Basics and Payoff Profiles

Treating the premium as part of the payoff.
Payoff diagrams and profit diagrams look alike, and the two words are used loosely.
Fix: Payoff is the value at expiration only. Profit equals payoff minus the premium paid (or plus premium received for a writer).
Using the call rule for a put moneyness test.
Students memorise S > K as ITM and apply it to every option.
Fix: A put is ITM when S < K. Ask whether exercising would give you something.
Forgetting to flip the sign for a short position.
The max function is memorised for the holder only.
Fix: Compute the holder's payoff first, then negate. A writer's payoff is never positive.
Calling the whole premium of an ITM option time value.
Students confuse premium with time value.
Fix: Time value = premium − intrinsic value. An ATM or OTM option has zero intrinsic value, so its premium is all time value.
Thinking a long put has unlimited profit.
It is confused with the long call, or with shorting the stock.
Fix: The asset price cannot go below zero, so the long put's maximum payoff is K and maximum profit is K − premium.
Computing breakeven as K − premium for a call.
Direction of the adjustment is mixed up.
Fix: The call needs S to rise above K by the premium. Breakeven is K + premium. For a put, it is K − premium.

Worked examples

Example 1

A trader buys a European call on a stock with strike $50 for a premium of $3.50. At expiration the stock is at $57. What are the trader's payoff and profit, and what is the profit of the writer?

Show the solution

Long call payoff = max(57 − 50, 0) = $7.00.
Long profit = 7.00 − 3.50 = $3.50.
Writer's payoff = −$7.00.
Writer's profit = −7.00 + 3.50 = −$3.50, the negative of the holder's profit.

Answer: Payoff $7.00, profit $3.50 for the holder. The writer loses $3.50.

Example 2

A European put has strike $80 and was bought for $4. Today the stock trades at $75 and the put is quoted at $8. (a) Is the put ITM, ATM or OTM? (b) What are its intrinsic value and time value? (c) What is the breakeven price at expiration, and what is the buyer's profit if the stock ends at $90?

Show the solution

(a) A put is ITM when S < K. Since 75 < 80, the put is in the money.
(b) Intrinsic value = max(80 − 75, 0) = $5. Time value = 8 − 5 = $3.
(c) Breakeven = K − premium = 80 − 4 = $76.
At S_T = 90, the put payoff = max(80 − 90, 0) = 0.
Profit = 0 − 4 = −$4, the full premium paid.

Answer: (a) In the money. (b) Intrinsic value $5, time value $3. (c) Breakeven $76; at $90 the buyer loses $4.

Exam tips

Read the question for the side: long or short, call or put. Most wrong answers come from the wrong sign.
Check whether the question asks for payoff or profit. The numeric difference is the premium.
Use the bounds as a filter: a long option's loss is limited to its premium, and a short option's gain is limited to its premium.
For moneyness questions, apply the test to the option type, and use today's price S, not the premium.
Unless told otherwise, ignore interest on the premium. If the question asks to compound it, multiply the premium by the growth factor before subtracting.

Practice questions from Properties of Options

Option Basics and Payoff Profiles in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Option Basics and Payoff Profiles: frequently asked questions

What is the difference between option payoff and option profit?

Payoff is the cash value of the option at expiration, before considering what you paid for it. Profit is payoff minus the premium paid for a long position. For a writer, profit is the premium received minus the payoff made to the holder.

What is the difference between intrinsic value and time value?

Intrinsic value is the amount the option would pay if exercised now: max(S − K, 0) for a call and max(K − S, 0) for a put. Time value is the premium minus intrinsic value. It reflects the chance that the option moves further into the money before expiry, and it is zero at expiration.

How do I tell if an option is in the money, at the money or out of the money?

Compare the current asset price S with the strike K. A call is ITM when S > K and OTM when S < K. A put is ITM when S < K and OTM when S > K. Both are ATM when S = K.

Which positions have unlimited loss?

The short call has theoretically unlimited loss because the asset price has no upper limit. The short put has a large but limited loss, since the price cannot fall below zero. Long positions lose at most the premium paid.