Pricing and Valuation of Options

Derivatives, LOS weight share 0.8 percent of the 365 Level I learning outcomes.

DerivativesPricing and Valuation of Options

Time value is positive for almost every option right up until the final second before expiration, and the exam's cleanest trap is a candidate who sees an at-the-money option and assumes, because its intrinsic value is zero, that the option itself must be worth nothing.

Before you watch

Answer these three first. Getting them wrong now is normal, and it helps the lesson stick. Reveal the answers when you're done, then read on.

1. A call option with strike $75 is trading at $9 while the underlying is at $80. The option's time value is closest to:

Answer: C. Intrinsic value = max(S - X, 0) = max(80 - 75, 0) = $5. Time value = option price - intrinsic value = 9 - 5 = $4. Time value is a distinct component from intrinsic value, not the full option price and not the intrinsic value itself.

2. All else equal, an increase in the volatility of the underlying asset will most likely:

Answer: A. Higher volatility raises the probability of large favorable price moves for the holder of either a call or a put, since both option types have asymmetric payoffs (loss capped at the premium, upside participation unlimited or substantial); volatility therefore increases the value of both calls and puts, one of the few option-value factors that moves both types in the same direction.

3. The no-arbitrage price of a forward commitment and the no-arbitrage price of a contingent claim are both grounded in the same core principle, best described as:

Answer: B. Both forward commitments and contingent claims are priced using replication and no-arbitrage logic: if a portfolio of the underlying asset and risk-free borrowing or lending can be constructed to produce the identical payoff as the derivative, the derivative must be priced equal to that replicating portfolio, or a riskless arbitrage profit would be available.

The lesson

The video lesson for this unit is recorded and waiting to be published. Everything it teaches is written out below.

The reading

Five to ten minutes on this one unit: what the exam wants, the idea in plain words, then straight into the trap and the practice.

The exam wants you to calculate an option's intrinsic value and time value, classify moneyness correctly for both a call and a put, describe the six factors that move option prices and in which direction, and describe how both forward commitments and contingent claims are priced through a replicating portfolio.

An option's market price splits into exactly two components. Intrinsic value is what the option would be worth if exercised immediately: max(0, S - X) for a call, max(0, X - S) for a put. Time value is everything left over once intrinsic value is subtracted from the option's actual price. Time value is generally positive for any option before expiration and reaches zero only at expiration itself, because it reflects the real, ongoing chance the option finishes further in the money before time runs out. An at-the-money option has zero intrinsic value by definition. That is exactly the case that tempts a candidate into assuming the option itself must be worth nothing. It still carries positive time value right up until the final moment.

Moneyness compares the underlying price to the strike, and the direction flips entirely between a call and a put, which is the module's most repeated trap. A call is in the money when the underlying price is above the strike, at the money when the two are equal, and out of the money when the underlying sits below the strike. A put runs the exact opposite direction: in the money when the underlying is below the strike, out of the money when it is above. Applying a call's moneyness rule to a put question, especially right after working several call questions in a row, is a frequent, avoidable error.

Six factors move an option's value, and each factor's direction must be memorized on its own rather than assumed to run the same way for both option types. A higher underlying price raises call value and lowers put value; a higher strike price does the reverse. More time to expiration raises the value of both, since more time simply means more opportunity for a favorable move either way. Higher volatility raises the value of both as well. That is the factor candidates most often get backward, since volatility widens the range of favorable outcomes for any option holder regardless of direction. A higher risk-free rate raises call value and lowers put value, through its effect on the present value of the strike price paid or received later. Dividends lower call value and raise put value, because the underlying's price drops on the ex-dividend date. Time and volatility are the only two factors that help both option types at once; the other four each help one type and hurt the other.

Both forward commitments and contingent claims are priced through the same underlying logic, replication and no-arbitrage, even though the specific replicating portfolio differs by instrument type. A forward commitment is priced by finding the portfolio of the underlying asset and risk-free borrowing or lending that replicates its fixed, symmetric payoff. A contingent claim is priced the same way, but the replicated payoff is asymmetric and contingent instead. That generally requires the replicating position to be adjusted as the underlying price moves, which is exactly why option pricing is structurally harder than forward pricing even though both rest on the same no-arbitrage foundation.

A call option's payoff diagram, kinked at the strike price payoff underlying price strike price expires worthless gains dollar for dollar
Below the strike, the option is worth nothing at expiration; above it, its value rises dollar for dollar with the underlying. The kink sits exactly at the strike price.

Worked in full

A put option with a strike price of $60 is trading at $7. The underlying stock is at $55. What is the option's intrinsic value and time value? Intrinsic value (put) = max(0, X - S) = max(0, $60 - $55) = $5. Time value = option price - intrinsic value = $7 - $5 = $2. The put is $5 in the money, and the remaining $2 of its price reflects time value, the chance the stock falls further before expiration.

The same problem, one step removed

Same option: put, strike $60, trading at $7, underlying at $55. Compute intrinsic value using the put formula first, then subtract from the option's price to isolate time value yourself.

The trap

An at-the-money option has zero intrinsic value by definition, which tempts a candidate into assuming the option itself is worthless; it still carries positive time value right up until expiration, since a real chance of finishing in the money remains.

Learning outcomes covered by this module

Verbatim from the 2026 CFA Level I topic outline. Every practice question and key rule below is tagged to one of these where the stem and explanation make the match clear.

  1. explain the exercise value, moneyness, and time value of an option
  2. contrast the use of arbitrage and replication concepts in pricing forward commitments and contingent claims
  3. identify the factors that determine the value of an option and describe how each factor affects the value of an option

Key rules

Written from this module's own lesson and the 2026 CFA Level I topic outline, in teaching order, each tagged to the learning outcome it belongs to where that is clear.

LOS 01

An option's price decomposes into exactly two components: intrinsic value and time value

Intrinsic value is the exercise value, what the option would be worth if exercised immediately: max(0, S - X) for a call, max(0, X - S) for a put. Time value is whatever is left over, the option's current market price minus its intrinsic value, and it reflects the remaining possibility that the option finishes further in the money before expiration. Time value is generally positive for any option with time remaining before expiration, including an at-the-money option with zero intrinsic value; confusing zero intrinsic value with zero total value is a direct and common error.

LOS 01

Moneyness classifies an option purely by comparing the underlying price to the strike, and the direction is opposite for calls and puts

A call is in the money when S is greater than X, at the money when S equals X, and out of the money when S is less than X. A put is in the money when S is less than X, at the money when S equals X, and out of the money when S is greater than X, the exact reverse direction from a call. Applying the call's moneyness rule to a put question, or vice versa, is one of the most frequent classification errors on this topic.

LOS 02

Both forward commitments and contingent claims are priced through replication and no-arbitrage, though the specific replicating portfolio differs by instrument type

A forward commitment (forward, future, or swap) is priced by finding the portfolio of the underlying and risk-free borrowing or lending that replicates its fixed, symmetric payoff; a contingent claim (an option) is priced by finding a portfolio of the underlying and risk-free borrowing or lending that replicates its asymmetric, contingent payoff, generally requiring the replicating position to be adjusted as the underlying price and time to expiration change. In both cases, if the derivative's market price diverges from the cost of its replicating portfolio, an arbitrageur can transact in both simultaneously to lock in a riskless profit, and this pressure drives the derivative's price back to the no-arbitrage value.

LOS 03

Six factors determine an option's value, and each factor's direction of effect must be memorized individually rather than assumed to be symmetric between calls and puts

The underlying asset's price raises call value and lowers put value; the strike price lowers call value and raises put value; more time to expiration raises the value of both (more opportunity for favorable moves); higher volatility raises the value of both (larger potential favorable moves for either payoff direction); a higher risk-free rate raises call value and lowers put value (through its effect on the present value of the strike price); and dividends expected on the underlying lower call value and raise put value (since the option holder does not receive dividends the spot holder would). Only time and volatility move both option types in the same direction; every other factor moves calls and puts in opposite directions.

The trick

Authored only where a key rule has an arbitrary number, list, or formula shape worth a memory device; a module with none of those has no tricks here, on purpose.

Zero intrinsic value does not mean zero total value

An at-the-money option has zero intrinsic value by definition, but it still has positive time value right up until expiration, since there remains a real chance it finishes in the money; the two components are separate.

Moneyness direction flips between calls and puts

Call ITM: S > X. Put ITM: S < X. A candidate who has just worked several call-moneyness questions is primed to misapply that same direction to a put question.

Only time and volatility move calls and puts the same direction; the other four factors split

Underlying price, strike, rate, and dividends each help one option type and hurt the other; time and volatility are the two factors that help both, since both simply widen the range of favorable outcomes for any option holder.

The method

Authored, ordered steps for answering this module's question types; a calculation module's calculator-dependent step ends with a bracketed BA II Plus keystroke sequence.

  1. For an intrinsic-versus-time-value question, compute intrinsic value first using the correct max() formula for the option type, then subtract from the given option price to isolate time value.
  2. For a moneyness question, write down S and X explicitly, then apply the call rule (ITM if S > X) or the put rule (ITM if S < X, the reverse), rather than relying on memory alone.
  3. For a replication/no-arbitrage question, identify that both forward commitments and contingent claims are priced by matching a replicating portfolio of the underlying plus risk-free borrowing or lending to the derivative's payoff.
  4. For a six-factor question, check whether the factor in question is time or volatility (helps both call and put) or one of the other four (helps one, hurts the other), rather than assuming a uniform direction.

One card

Condensed from the key rules and tricks above, nothing new. What you'd want on one index card the night before.

Practice questions

Pick an answer, say how sure you are, then reveal. Every wrong choice gets its own explanation. 10 question(s) available for this unit.

Question 1Exam level

An investor buys a call option on a stock with a strike price of $50 and pays a premium of $4. At expiration, the stock price is $58. The profit per share to the call buyer is closest to:

How sure are you?

Correct: A. The correct answer is $4. Profit = max(S - X, 0) - premium = max(58 - 50, 0) - 4 = 8 - 4 = $4. The payoff is $8 but the profit nets out the $4 premium paid..
B. This is the gross payoff. Max(58-50, 0) = $8. You might stop here and forget to subtract the premium. Payoff is gross. Profit requires subtracting the premium cost of acquiring the option.
C. A candidate might think the premium makes the position a net loss without computing the payoff first. The call is exercised for a positive payoff of $8, which more than offsets the $4 premium.

Unit: pricing-and-valuation-of-options

Question 2Exam level

A put option has a strike price of $60. The stock is currently trading at $55. The intrinsic value of the put is closest to:

How sure are you?

Correct: A. The correct answer is $5. Intrinsic value of a put = max(X - S, 0) = max(60 - 55, 0) = $5. The put is in-the-money by $5..
B. A candidate applying call-option logic would write max(S - X, 0) = max(55 - 60, 0) = 0. For puts, intrinsic value = max(X - S, 0). The formula runs in the opposite direction from calls.
C. A candidate might compute 55 - 60 = -5 without applying the max(.,0) floor. Intrinsic value is floored at zero. Options never have negative intrinsic value. They simply expire worthless.

Unit: pricing-and-valuation-of-options

Question 3Exam level

A stock currently trades at $45. An investor writes (sells) a put option with a strike price of $50 and receives a premium of $6. If the stock price falls to $38 at expiration, the profit to the put writer is closest to:

How sure are you?

Correct: A. The correct answer is -$6. Put writer profit = premium received - max(X - S, 0) = 6 - max(50 - 38, 0) = 6 - 12 = -$6. The buyer exercises, forcing the writer to buy at $50 when the stock is worth $38..
B. A candidate focused only on the premium received, forgetting the put was exercised against the writer. The put is deep in-the-money at $38 vs $50 strike. The writer is obligated to buy at $50, losing $12 before netting the premium.
C. Arithmetic error: computing 45 - 38 = 7 and using the original stock price instead of the strike. The relevant comparison is strike ($50) vs expiration price ($38), not current price vs expiration price.

Unit: pricing-and-valuation-of-options

Question 4Exam level

Which of the following statements best describes a long call position?

How sure are you?

Correct: A. The correct answer is The right to buy a specified quantity at the exercise price before or at expiration. A call option gives the buyer (long) the right. Not the obligation. To BUY the underlying at the strike price..
B. This describes the short put writer's obligation. 'obligation' sounds right because options involve obligations somewhere. The BUYER of a call has a right, not an obligation. The writer of a put has the obligation to buy if exercised.
C. This describes the short call writer's obligation, which is the counterparty to the long call. Long = buyer = right holder. Short = writer = obligation bearer. The question asks about long (buyer) position.

Unit: pricing-and-valuation-of-options

Question 5Exam level

A call option with a strike price of $75 is trading at $9. The underlying stock is at $80. The time value of the option is closest to:

How sure are you?

Correct: A. The correct answer is $4. Intrinsic value = max(S - X, 0) = max(80 - 75, 0) = $5. Time value = option price - intrinsic value = 9 - 5 = $4..
B. This is the intrinsic value. Candidates who correctly compute max(80-75,0) confuse intrinsic for time value. Intrinsic value = $5. Time value = $9 - $5 = $4. These are different components.
C. Adding the stock-strike gap ($5) to the option price ($9). Nonsensical but arithmetically close. Time value is never larger than the option price. Adding intrinsic to the total price is a double-count error.

Unit: pricing-and-valuation-of-options

Question 6Exam level

At expiration, the payoff to the writer of a call option with a strike price of $40 when the stock price is $47 is closest to:

How sure are you?

Correct: A. The correct answer is -$7. Short call payoff at expiration = -max(S - X, 0) = -max(47 - 40, 0) = -$7. The writer must deliver shares at $40 when they are worth $47..
B. This is the BUYER's payoff, not the writer's. Candidates who compute long call payoff and forget to flip the sign. Short positions have mirror-image payoffs. Writer's payoff = negative of buyer's payoff.
C. The strike price itself is a plausible-looking distractor. The payoff is not the strike price. It is the loss from being forced to sell at $40 when shares are worth $47.

Unit: pricing-and-valuation-of-options

Question 7Harder

All else equal, which of the following changes would most likely increase the value of a put option?

How sure are you?

Correct: A. The correct answer is An increase in volatility of the underlying. Increased volatility increases the value of BOTH calls and puts because it raises the probability of the option expiring deeply in-the-money..
B. You might sometimes confuse time decay direction, or think 'closer to expiry = closer to payout.'. Less time means less opportunity for favorable moves. Time value erodes as expiration approaches.
C. Higher rates are often associated with higher returns on financial instruments generally. Higher risk-free rates REDUCE put value because the present value of the exercise price (what the put delivers) falls. This is the #1 tested counterintuitive factor direction.

Unit: pricing-and-valuation-of-options

Question 8Exam level

A stock is trading at $100. An investor holds 100 shares and buys 1 put contract (100 shares) with strike price $95 for a premium of $3 per share. The maximum loss on the combined stock-plus-put position is most likely:

How sure are you?

Correct: A. The correct answer is $800. Maximum loss = (current price - strike price + premium) x shares = (100 - 95 + 3) x 100 = $800. The put floors the sale price at $95, so the maximum loss is the $5 decline allowed plus the $3 premium cost..
B. Only counting the premium cost ($3 x 100 shares), forgetting the $5 gap between current price and strike. The put does not protect at exactly the current price. It protects at the strike. The $5 unprotected gap is a deductible.
C. Confusing unhedged stock exposure (which is indeed large) with the hedged position. The whole point of the protective put is to cap the downside. The put converts unlimited stock downside into a bounded loss.

Unit: pricing-and-valuation-of-options

Question 9Above the exam

Two otherwise identical call options on the same non-dividend-paying stock differ only in time to expiration: Option A expires in 3 months, Option B expires in 9 months. Combining the components of an option's value (intrinsic value plus time value) with how time to expiration affects time value, Option B's premium relative to Option A's should most likely be:

How sure are you?

Correct: B. An option's total value is intrinsic value plus time value. With the same strike and current stock price, both options have identical INTRINSIC value today, but Option B's longer time to expiration gives the underlying stock more opportunity to move favorably before expiration, which increases its TIME value component. All else equal, more time to expiration increases an option's premium (for standard American and most European options on non-dividend-paying stocks), so Option B should trade at a higher premium than Option A.
A. Longer time to expiration generally INCREASES, not decreases, an option's value, because it increases the time value component; claiming the opposite reverses one of the most basic relationships in option pricing.
C. Intrinsic value is only ONE of the two components of an option's premium; time value, which depends heavily on time to expiration (among other factors like volatility), is the other component, and it is exactly what differs between these two otherwise identical options.

Unit: pricing-and-valuation-of-options

Question 10Above the exam

A call option and a put option on the same stock share the same strike price and expiration date. The stock pays no dividends. Combining put-call parity with the specific effect of an increase in the risk-free interest rate, holding all else (stock price, strike, volatility, time) constant, an increase in the risk-free rate should most likely:

How sure are you?

Correct: A. Put-call parity (C + PV(X) = P + S) shows that the present value of the strike price is a key link between call and put values. A higher risk-free rate LOWERS the present value of the strike price (PV(X) falls); since S (stock price) is unchanged, and C + PV(X) = P + S must still hold, a lower PV(X) means C must rise relative to P (or equivalently, holding the relationship, a higher rate increases call values and decreases put values, since a call holder benefits from a cheaper effective strike price paid later, while a put holder's fixed future strike proceeds are worth less today).
B. The two options do not move in the same direction with a change in the risk-free rate; put-call parity shows they move in OPPOSITE directions as PV(X) changes, since the rate affects the present value of the fixed strike price differently for the right to BUY (call) versus the right to SELL (put) at that strike.
C. The risk-free rate is one of the recognized factors that determines option value (alongside stock price, strike, volatility, time, and dividends); put-call parity itself demonstrates the rate's role through the PV(X) term, so claiming no effect contradicts that basic relationship.

Unit: pricing-and-valuation-of-options

Your results

Answer the questions above, then press the button.

Not yet scored