Lesson 1 of 3 6–9% of the exam

By Daniil Tarakanov Updated Oct 20, 20262027 curriculum

Exercise value, moneyness and time value

Q: What is the difference between exercise value and time value of an option?

Exercise value is what the option would be worth if exercised now: max(0, S − PV(X)) for a call, max(0, PV(X) − S) for a put. Time value is the rest of the price, paid for the chance the option ends further in the money. Price = exercise value + time value.

Q: How do you know if an option is in the money?

Compare the underlying price S with the exercise price X. A call is in the money when S > X, a put when S < X. At the money means S = X, and anything else is out of the money.

Q: Why does an option's time value decay?

Time value pays for the chance of a favorable move before expiry. As the remaining time shrinks, that chance shrinks, and at expiration only the payoff is left. The decay costs the option buyer and benefits the seller.

An option's price splits into exercise value, what it would be worth if exercised now (using the present value of the exercise price), and time value, the extra paid for the chance it ends further in the money. Moneyness says whether exercising now would pay.

8 min cram, 34 min full read. Based on the 2027 CFA® Program Level I curriculum, Derivatives, Learning Module 8. Also part of the 2026 curriculum, so it applies to the November 2026 exam too.

Tailor this to you: take the self-assessment

Before this: Forwards, Futures, Swaps, Options and Credit Derivatives, Arbitrage, Replication and the Cost of Carry

On the exam

Explain the exercise value, moneyness, and time value of an option

Explain the exercise value, moneyness and time value of an option. Expect: compute exercise value and time value from a quoted price using the present value of the exercise price, and classify an option as in, at or out of the money.

How deeply to learn each part

Know the idea: Understand it in general. It frames other topics, but you will not calculate with it.
Use it: Understand it well enough to solve a question with it. Recognize when it applies.
Memorize: Learn it by heart. The exam will not give it to you.

You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.

You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.

What is an option’s price made of?

An option’s price has two parts, and the exam wants you to split it. The exercise value is what the option would be worth if it could be exercised right now. The time value is everything else the buyer pays for: the chance that the option ends up worth more than that.

What an option price is made of

Option price todayprice = exercise value + time value

Exercise value Memorize what exercising now would be worth
- Call Memorize max(0, S − PV(X))
- Put Memorize max(0, PV(X) − S)
Time value Memorize price minus exercise value
- Never negative the holder can always walk away
- Decays to zero at expiration Use it time value decay

This lesson covers European options, which can be exercised only at expiration. Before expiry they still trade, at a price that reflects the payoff the market expects.

How do you compute the exercise value?

Memorize

At expiration the holder exercises only if it pays: a call pays S_T − X, a put pays X − S_T. If neither is positive the option expires worthless and the buyer’s loss is the premium.

Before expiry, the curriculum values the exercise price in today’s money. The strike is paid (call) or received (put) at expiration, so what counts is the present value of the exercise price , PV(X) = X(1 + r)^−(T − t), where T − t is the time left.

Exercise value of a call Memorize

EV_c = \max\left(0,\ S_t - X(1 + r)^{-(T-t)}\right)

Exercise value of a put Memorize

EV_p = \max\left(0,\ X(1 + r)^{-(T-t)} - S_t\right)

Exercise value at expiration Memorize

EV_c = \max(0,\ S_T - X), \qquad EV_p = \max(0,\ X - S_T)

At expiration T − t = 0, so PV(X) = X and the two versions agree.

Exam tip Some study material uses S − X before expiry. For the 2026 exam, when a question gives a rate and a time, use PV(X).

Rearrange itCall exercise value: solve for any input

The question asks for

A European call has an exercise price of 80.00 and 0.75 years to expiration. The risk-free rate is 4.00%, the underlying is at 88.00 and pays no income. The exercise value of the call is closest to:

Underlying price, S_tExercise price, XRisk-free rate, r (annual)%Time to expiration, T − t (years)

E V_{c} = max (0, S_{t} - X (1 + r)^{- (T - t)})

max(0, 88.00 − 80.00 × (1 + 0.04)^−0.75) = max(0, 88.00 − 77.68) = 10.32

Exercise value of the call10.32

On your calculator

1.04y^x0.75+|-=×80=PV(X) = 77.681
+|-+88=10.319

y^x power · +|- change sign

1.04ENTER0.75CHSy^x80×PV(X) = 77.681
CHS88+10.319

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · y^x power

Rearrange itPut exercise value: solve for any input

The question asks for

A European put has an exercise price of 80.00 and 0.75 years to expiration. The risk-free rate is 4.00%, the underlying is at 74.00 and pays no income. The exercise value of the put is closest to:

Underlying price, S_tExercise price, XRisk-free rate, r (annual)%Time to expiration, T − t (years)

E V_{p} = max (0, X (1 + r)^{- (T - t)} - S_{t})

max(0, 80.00 × (1 + 0.04)^−0.75 − 74.00) = max(0, 77.68 − 74.00) = 3.68

Exercise value of the put3.68

On your calculator

1.04y^x0.75+|-=×80=PV(X) = 77.681
−74=3.681

y^x power · +|- change sign

1.04ENTER0.75CHSy^x80×PV(X) = 77.681
74−3.681

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · y^x power

What do in, at and out of the money mean?

Moneyness compares the underlying price with the exercise price. It tells you whether exercising would pay. An option is in the money (ITM) when exercising would pay, at the money (ATM) when S = X, and out of the money (OTM) when exercising would not pay.

	Call	Put
In the money (ITM)	S > X	S < X
At the money (ATM)	S = X	S = X
Out of the money (OTM)	S < X	S > X

Moneyness: where the underlying sits against the exercise price

Underlying price S against exercise price Xwould exercising pay?

In the money (ITM) Memorize call: S > X; put: S < X
- Deep in the money Know the idea near one-for-one with the underlying
At the money (ATM) Memorize S = X for both
Out of the money (OTM) Memorize call: S < X; put: S > X
- Deep out of the money Know the idea barely reacts to the underlying

Moneyness also tells you how sensitive the option’s price is. A deep-in-the-money option is very likely to be exercised, so its price moves almost one-for-one with the underlying. A deep-out-of-the-money option is very unlikely to be exercised and barely reacts. For an at-the-money option, a small move in the underlying often decides whether it is exercised at all.

InteractivePrice = exercise value + time value

Try this 0 of 3

Slide the time left all the way to zero
Move S_t until the option is out of the money with zero exercise value
With the call and time left, set S_t between PV(X) and X

The dark hockey stick is what the option would be worth exercised now; the curve is its price. Drag S_t, then slide the time left down to zero.

Call value against S_t, 0.75 years leftExercise 10.32 · Price 12.50

The exercise value line is flat at zero below PV(X) = 77.68 and rises one for one above it. The price curve lies above it everywhere; the gap is time value, largest near the kink. At S_t = 88: exercise value USD 10.32, price USD 12.50, time value USD 2.18 (in the money).

USD 12.50 price = USD 10.32 exercise value + USD 2.18 time value

USD 10.32 of the USD 12.50 price is real today; the other USD 2.18 is time value, the chance of ending further in the money.

The curve comes from an option pricing model and is for illustration (the model itself is not examined at Level I). Moneyness compares S_t with X; the exercise value before expiry compares S_t with PV(X), as in the 2026 curriculum.

Option

Underlying price today, S_tUSD 88

Exercise price, XUSD 80

Time left to expiry, T − t (years)0.75 years

Risk-free rate, r4%

Volatility of the underlying20.9%

PV(X)USD 77.68

Exercise valueUSD 10.32

Option priceUSD 12.50

Time valueUSD 2.18

MoneynessIn the money

Show working

PV(X) = X × (1 + r)^−(T − t) = 80 × 1.04^−0.75 = 77.68

Call exercise value = max(0, 88 − 77.68) = 10.32

Price (from the curve at 20.9% volatility) = 12.50

Time value = price − exercise value = 12.50 − 10.32 = 2.18

Moneyness: a call with S_t = 88 and X = 80 is in the money.

Exercise and time value on your calculator

1.04y^x0.75=1/x×80=77.68, PV(X)
+|-+88=10.32, the exercise value
+|-+12.50=2.18, the time value

y^x power · 1/x reciprocal · +|- change sign

88ENTER80ENTER1.04ENTER0.75y^x÷−10.32, the exercise value
CHS12.50+2.18, the time value

ENTER enter (on the HP, puts the number on the stack) · y^x power · CHS change sign

Display: 2.18 time value

Price = what it is worth now + what it might become; the second part melts to zero by expiry.

How do you find the time value?

Memorize

Time value is the price minus the exercise value. It is never negative, because the holder can always walk away and lose nothing more than the premium. It shrinks as expiry nears, a process called time value decay , and is zero at expiration.

Option price = exercise value + time value Memorize

c_t = EV_c + TV, \qquad p_t = EV_p + TV, \qquad TV = \text{price} - EV \ge 0

Worked example Splitting two quoted prices

Use the options from the earlier example. The call (S_t = USD 88) trades at USD 12.50. The put (S_t = USD 74) trades at USD 9.00.

Call: time value = 12.50 − 10.32 = USD 2.18.
Put: time value = 9.00 − 3.68 = USD 5.32.
When the exercise value is zero, the whole price is time value. That holds for every out-of-the-money put, and for a call whenever S is at or below PV(X). (A call with S between PV(X) and X is out of the money yet has a small positive exercise value under the 2026 convention.)

Step 1 on your calculator

1.04y^x0.75+|-=×80= 77.68
+|-+88= 10.32
+|-+12.5= 2.18

y^x power · +|- change sign

1.04ENTER0.75CHSy^x80× 77.68
CHS88+ 10.32
CHS12.5+ 2.18

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · y^x power

Rearrange itPrice, exercise value and time value: solve for any input

The question asks for

An option trades at 12.50 and its exercise value is 10.32. Its time value is closest to:

Option priceExercise value

T V = c_{t} - E V

12.50 − 10.32 = 2.18

Time value2.18

On your calculator

12.5−10.319=2.181

12.5ENTER10.319−2.181

ENTER enter (on the HP, puts the number on the stack)

Time value decay is a cost to the buyer of an option and a benefit to the seller. As the days pass with the underlying unchanged, the buyer’s option loses value and the seller’s position gains.

Exam tip Check the order on every question: exercise value first (with PV(X)), then time value as price minus exercise value.

Go deeper Why the kink sits at PV(X), not X

Before expiry, a call is worth exercising only if the share costs more than the strike you will pay later, valued in today’s money. The break-even point is therefore S = PV(X), which is below X when interest rates are positive. Set X equal to the forward price F₀(T) and the call’s exercise value equals the value of a long forward, S_t − PV(F₀(T)), whenever that is positive. The option copies the forward on the upside and drops the downside.

Go deeper An option can be ITM by moneyness yet have zero exercise value

Moneyness compares S with X, but exercise value compares S with PV(X). A put with X = 40 and S = 39.80 is in the money by moneyness (S < X). With r = 4% and six months left, PV(X) = 39.22, which is below S, so the exercise value is zero and the whole price is time value. The curriculum treats such options this way, so follow the formula when a question gives you a rate.

Go deeper How moneyness links to the hedge ratio

The more likely exercise is, the more of the underlying a replicating portfolio must hold. That proportion, the hedge ratio, is close to 1 for a deep-in-the-money call, close to 0 for a deep-out-of-the-money call, and in between at the money. The binomial model lesson builds it.

Memorize this

MemorizeExercise value (2026 convention)

	Call	Put
Before expiry	$\max(0,\ S_t - PV(X))$	$\max(0,\ PV(X) - S_t)$
At expiry	$\max(0,\ S_T - X)$	$\max(0,\ X - S_T)$
Time value	price − exercise value	price − exercise value

Memory hook Call: what you get (the asset) minus what you pay (X, in today's money). Put is the mirror. At expiry the discounting disappears, so PV(X) becomes X.

Know it cold Before expiry use $PV(X) = X(1+r)^{-(T-t)}$ whenever a rate and time are given. Time value is never negative and is zero at expiry.

MemorizeMoneyness

	Call	Put
In the money	$S > X$	$S < X$
At the money	$S = X$	$S = X$
Out of the money	$S < X$	$S > X$

Memory hook A call is in the money when the asset costs more than the strike (you can buy it cheaper). A put is the reverse.

Know it cold Deep ITM: price moves almost one-for-one with the underlying. Deep OTM: barely moves. Zero exercise value (every OTM put; a call with S at or below PV(X)) means the whole price is time value.

What an option price is made of

Option price todayprice = exercise value + time value

Exercise value Memorize what exercising now would be worth
- Call Memorize max(0, S − PV(X))
- Put Memorize max(0, PV(X) − S)
Time value Memorize price minus exercise value
- Never negative the holder can always walk away
- Decays to zero at expiration Use it time value decay

Moneyness: where the underlying sits against the exercise price

Underlying price S against exercise price Xwould exercising pay?

In the money (ITM) Memorize call: S > X; put: S < X
- Deep in the money Know the idea near one-for-one with the underlying
At the money (ATM) Memorize S = X for both
Out of the money (OTM) Memorize call: S < X; put: S > X
- Deep out of the money Know the idea barely reacts to the underlying

Exercise value of a call

EV_c = \max\left(0,\ S_t - X(1 + r)^{-(T-t)}\right)

Quick example

Call, X = 50, S_t = 54, r = 3%, 0.5 years left. PV(X) = 50 × 1.03^−0.5 = 49.27. EV = 54 − 49.27 = 4.73.

On your calculator

1.03y^x0.5+|-=×50= 49.27
+|-+54= 4.73

y^x power · +|- change sign

1.03ENTER0.5CHSy^x50× 49.27
CHS54+ 4.73

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · y^x power

Exercise value of a put

EV_p = \max\left(0,\ X(1 + r)^{-(T-t)} - S_t\right)

Quick example

Put, X = 65, S_t = 60, r = 2%, 0.5 years left. PV(X) = 64.36. EV = 64.36 − 60 = 4.36.

On your calculator

1.02y^x0.5+|-=×65= 64.36
−60= 4.36

y^x power · +|- change sign

1.02ENTER0.5CHSy^x65× 64.36
60− 4.36

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · y^x power

Exercise value at expiration

EV_c = \max(0,\ S_T - X), \qquad EV_p = \max(0,\ X - S_T)

Quick example

At expiration X = 80 and S_T = 91. Call: 11. Put: 0.

Option price = exercise value + time value

c_t = EV_c + TV, \qquad p_t = EV_p + TV, \qquad TV = \text{price} - EV \ge 0

Quick example

A call trades at 6.35 and its exercise value is 4.90. Time value = 6.35 − 4.90 = 1.45.

On your calculator

6.35−4.9= 1.45

6.35ENTER4.9− 1.45

ENTER enter (on the HP, puts the number on the stack)

How it is asked

Time value from a quoted price

Put X = 90, three months, r = 3.5%, S = 84, price 8.30. Time value?

90 × 1.035^−0.25 = 89.23; EV = 5.23; TV = 8.30 − 5.23 = 3.07. Trap: using X, which gives 8.30 − 6.00 = 2.30.
Classify moneyness

Call with X = 50 while the underlying is 46.

S < X, so a call is out of the money. Trap: reading the put rule for a call.
Time passes, nothing else changes

What happens to time value as expiry approaches?

It decays toward zero. It never turns negative.
Option that looks ITM but has zero exercise value

Put X = 40, S = 39.80, r = 4%, six months.

S < X so ITM by moneyness, but PV(X) = 39.22 < S, so exercise value is 0 and the whole price is time value.

Exam traps

Using X instead of PV(X) when a rate and a time to expiry are given (2026 convention).
Saying time value can be negative. It is zero at expiry and positive before.
Calling a put in the money when S > X. A put is in the money when S < X.
Treating the option's price as its exercise value. The price also holds time value.

Checkpoint

5 exam-style questions. About 90 seconds each.

1A put has an exercise price of EUR 120, six months to expiry, and the risk-free rate is 3%. The underlying trades at EUR 112 and pays no income. The put trades at EUR 10.20. Its time value is closest to:
2A call with an exercise price of 50 when the underlying is trading at 46 is:
3As a European option approaches expiration with everything else unchanged, its time value will most likely:
4A European call has an exercise price of 45 and 0.4 years to expiry. The risk-free rate is 2.5%, the underlying trades at 52 and pays no income, and the call trades at 8.60. The call's time value is closest to:
5A European put has an exercise price of 60 and six months to expiry. The risk-free rate is 3%, the underlying trades at 59.50 and pays no income, and the put trades at 1.90. Using the present-value convention, the put's moneyness, exercise value and time value are best described as:

Key takeaways

Exercise value before expiry uses PV(X): call max(0, S − PV(X)), put max(0, PV(X) − S).
Price = exercise value + time value. Time value is never negative and decays to zero at expiry.
ITM call: S > X. ITM put: S < X. ATM: S = X.
An option with zero exercise value is all time value: every out-of-the-money put, and a call with S at or below PV(X).

Exercise value of a call

EV_c = \max\left(0,\ S_t - X(1 + r)^{-(T-t)}\right)

Quick example

Call, X = 50, S_t = 54, r = 3%, 0.5 years left. PV(X) = 50 × 1.03^−0.5 = 49.27. EV = 54 − 49.27 = 4.73.

On your calculator

1.03y^x0.5+|-=×50= 49.27
+|-+54= 4.73

y^x power · +|- change sign

1.03ENTER0.5CHSy^x50× 49.27
CHS54+ 4.73

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · y^x power

Exercise value of a put

EV_p = \max\left(0,\ X(1 + r)^{-(T-t)} - S_t\right)

Quick example

Put, X = 65, S_t = 60, r = 2%, 0.5 years left. PV(X) = 64.36. EV = 64.36 − 60 = 4.36.

On your calculator

1.02y^x0.5+|-=×65= 64.36
−60= 4.36

y^x power · +|- change sign

1.02ENTER0.5CHSy^x65× 64.36
60− 4.36

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · y^x power

Exercise value at expiration

EV_c = \max(0,\ S_T - X), \qquad EV_p = \max(0,\ X - S_T)

Quick example

At expiration X = 80 and S_T = 91. Call: 11. Put: 0.

Option price = exercise value + time value

c_t = EV_c + TV, \qquad p_t = EV_p + TV, \qquad TV = \text{price} - EV \ge 0

Quick example

A call trades at 6.35 and its exercise value is 4.90. Time value = 6.35 − 4.90 = 1.45.

On your calculator

6.35−4.9= 1.45

6.35ENTER4.9− 1.45

ENTER enter (on the HP, puts the number on the stack)

All Derivatives formulas, every lesson

Practice exam-style questions on Pricing and Valuing Options

Next lesson Option price bounds and replication vs forwards

Questions about this lesson?

Where this comes back

Put–Call Parity and Option Replication Derivatives
The One-Period Binomial Model Derivatives

Questions candidates ask

What is the difference between exercise value and time value of an option?

Exercise value is what the option would be worth if exercised now: max(0, S − PV(X)) for a call, max(0, PV(X) − S) for a put. Time value is the rest of the price, paid for the chance the option ends further in the money. Price = exercise value + time value.

How do you know if an option is in the money?

Compare the underlying price S with the exercise price X. A call is in the money when S > X, a put when S < X. At the money means S = X, and anything else is out of the money.

Why does an option's time value decay?

Time value pays for the chance of a favorable move before expiry. As the remaining time shrinks, that chance shrinks, and at expiration only the payoff is left. The decay costs the option buyer and benefits the seller.

Spotted an error? Tell us and we will fix it.