Overview
Derivatives is 5-10% of the CFA Level 2 exam and advances from Level 1's conceptual introduction into pricing and valuing derivatives. It has three areas. Pricing and valuation of forward commitments cover how forwards, futures and swaps are priced at inception (the no-arbitrage price) and valued during their life as market conditions change, including interest rate, currency and equity forwards and swaps. Valuation of contingent claims covers valuing options using no-arbitrage principles, the factors determining option value, and put-call parity. The binomial model and option strategies cover the one- and two-period binomial option pricing model (using risk-neutral probabilities) and the use of option strategies.
The exam rewards pricing a forward or swap, valuing it as conditions change, valuing an option with the binomial model, and applying put-call parity, all grounded in no-arbitrage. The material is calculation-oriented and tested in vignettes, building on the fixed-income term structure.
How it's tested
CFA Level 2 Derivatives questions give market data in a vignette and ask you to price a forward or swap, value it at a point in time, or value an option with the binomial model, so read the case, identify the model, and compute precisely.
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Price the forward commitment
A forward, future or swap situation is described, and you compute the no-arbitrage price at inception.
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Value over its life
An existing forward or swap is described, and you value it as conditions change.
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Value the option
An option situation is described, and you value it with the binomial model or apply put-call parity.
The exam gives the spot price, the risk-free rate and the time to expiration and asks for the no-arbitrage forward price. The forward price is set so no riskless profit is possible: the spot price compounded at the risk-free rate over the contract's life, adjusted for any carry. Computing the forward price this way, by no-arbitrage at inception, is the approach the exam expects.
Topic areas 3
Official topic areas from the CFA Institute outline, in outline order.
8.1 Pricing and valuation of forward commitmentsPricing and valuing forwards, futures and swaps.
- What it means
- This covers the no-arbitrage pricing of forward commitments at inception and their valuation during their life: the forward price (spot compounded at the risk-free rate, adjusted for carry), how a forward or futures contract gains or loses value as the underlying moves, and the pricing and valuation of swaps (such as interest rate swaps as a series of forward rates or as bonds).
- What to understand
- At inception, a forward's price is set by no-arbitrage so the contract has zero value; afterward, its value changes as the spot and rates move. A swap's fixed rate is set so the swap's initial value is zero, and it is valued over its life as rates change. Distinguishing the price (fixed at inception) from the value (changing) is the key concept, and the calculations are tested.
- How it shows up
- A forward, future or swap situation is described, and you must price it at inception or value it over its life.
- Common confusion
- Confusing the forward price (set at inception) with the forward value (changing), or mispricing a swap.
8.2 Valuation of contingent claims (options)Option value drivers and put-call parity.
- What it means
- This covers valuing options using no-arbitrage principles, the factors that determine option value (underlying price, strike, time to expiration, volatility, risk-free rate, and cash flows on the underlying), the bounds on option prices, and put-call parity, the no-arbitrage relationship linking a call, a put, the underlying and a risk-free bond.
- What to understand
- Option value depends on several factors, rising with volatility and (for calls) time. Put-call parity states that a call plus a risk-free bond equals a put plus the underlying (for European options with the same strike and maturity), so the four instruments are priced consistently. Knowing the value drivers and applying put-call parity to find a missing price is tested.
- How it shows up
- An option situation is described, and you must identify a value driver or apply put-call parity.
- Common confusion
- Misapplying put-call parity (which instruments are on which side), or misjudging a value driver's effect.
8.3 The binomial model and option strategiesBinomial option pricing and strategies.
- What it means
- This covers the binomial option pricing model: the one-period and two-period models, modeling the underlying's up and down moves, using risk-neutral probabilities to value the option as the discounted expected payoff, and the use of option strategies (combinations of options and the underlying).
- What to understand
- The binomial model values an option by building a tree of possible underlying prices, computing the option payoff at each final node, and discounting back using risk-neutral probabilities (not real probabilities) at the risk-free rate. This no-arbitrage approach extends to multiple periods. Option strategies combine positions for specific payoffs. Knowing how to build and solve a binomial tree is heavily tested.
- How it shows up
- An option-pricing situation is described, and you must value the option with the binomial model or analyze a strategy.
- Common confusion
- Using real instead of risk-neutral probabilities, or misbuilding the binomial tree.
High-yield concepts
The terms, rules and formulas this domain turns into questions most often.
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Forward price vs. value
Set at inception versus changing.
- Remember
- Price fixed, value moves.
- Tested as
- Forward questions.
- Trap
- Confusing the two.
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No-arbitrage pricing
Prices prevent riskless profit.
- Remember
- The basis of valuation.
- Tested as
- Pricing questions.
- Trap
- Ignoring arbitrage.
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Forward price formula
Spot compounded at risk-free rate.
- Remember
- Adjusted for carry.
- Tested as
- Forward questions.
- Trap
- Omitting carry.
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Swap pricing
Fixed rate for zero initial value.
- Remember
- Valued as rates change.
- Tested as
- Swap questions.
- Trap
- Mispricing the swap.
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Option value drivers
Price, strike, time, volatility, rate.
- Remember
- Volatility raises value.
- Tested as
- Option questions.
- Trap
- Ignoring a driver.
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Put-call parity
Call plus bond equals put plus underlying.
- Remember
- No-arbitrage link.
- Tested as
- Option questions.
- Trap
- Misarranging the instruments.
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Binomial model
Tree of up and down moves.
- Remember
- Discount risk-neutral payoffs.
- Tested as
- Option questions.
- Trap
- Misbuilding the tree.
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Risk-neutral probabilities
Used to value options.
- Remember
- Not real-world probabilities.
- Tested as
- Option questions.
- Trap
- Using real probabilities.
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Discount at risk-free rate
Binomial valuation uses the risk-free rate.
- Remember
- With risk-neutral probabilities.
- Tested as
- Option questions.
- Trap
- Using a risky rate.
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Option strategies
Combinations of options.
- Remember
- For specific payoffs.
- Tested as
- Strategy questions.
- Trap
- Misreading the payoff.
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Zero value at inception
A fair forward or swap.
- Remember
- Value starts at zero.
- Tested as
- Forward questions.
- Trap
- Expecting nonzero value.
Side by side
Concepts candidates mix up, compared on the point that decides the answer.
Forward price vs. forward value
| Concept | Meaning | Key difference | Common trap |
|---|---|---|---|
| Forward price | Set at inception by no-arbitrage | Fixed for the contract | Confusing with value |
| Forward value | Changes as the spot and rates move | Zero at inception | Confusing with price |
Real vs. risk-neutral probabilities
| Concept | Meaning | Key difference | Common trap |
|---|---|---|---|
| Risk-neutral | Used in option valuation | Discount at the risk-free rate | Using real probabilities |
| Real-world | Actual probabilities | Not used for no-arbitrage pricing | Using them in the binomial model |
Put-call parity components
| Concept | Meaning | Key difference | Common trap |
|---|---|---|---|
| Call plus bond | Fiduciary call | Equals a protective put | Misarranging |
| Put plus underlying | Protective put | Equals the fiduciary call | Misarranging |
Exam traps
Each trap is an answer that looks right. Learn the clue that should change your mind.
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Forward has value at inception
- What candidates pick
- Assume a newly initiated forward at the no-arbitrage price has positive value.
- Why it looks right
- It locks in a price.
- Why it's wrong
- A forward priced by no-arbitrage has zero value at inception; it gains or loses value only as the underlying and rates move afterward.
Clue to watch for The forward was just initiated at the fair price.
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Real probabilities in the tree
- What candidates pick
- Value an option in the binomial model using the real-world probabilities of up and down moves.
- Why it looks right
- They seem relevant.
- Why it's wrong
- No-arbitrage option valuation uses risk-neutral probabilities and discounts at the risk-free rate, not real-world probabilities.
Clue to watch for The binomial model is being used to value the option.
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Put-call parity misarranged
- What candidates pick
- Set a call plus the underlying equal to a put plus a bond.
- Why it looks right
- All four appear.
- Why it's wrong
- Put-call parity states a call plus a risk-free bond (present value of the strike) equals a put plus the underlying; the arrangement matters.
Clue to watch for The question asks to solve for a missing option price.
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Ignore carry in the forward price
- What candidates pick
- Price a forward on a dividend-paying stock as just the spot compounded.
- Why it looks right
- Compounding is the base.
- Why it's wrong
- The forward price must adjust for carry (dividends or income on the underlying), which reduces the forward price.
Clue to watch for The underlying pays dividends or income.
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Swap fixed rate is arbitrary
- What candidates pick
- Assume the swap's fixed rate can be set at any level.
- Why it looks right
- It is negotiated.
- Why it's wrong
- The swap's fixed rate is set by no-arbitrage so the swap has zero value at inception, based on the current term structure.
Clue to watch for The swap is initiated at a fair rate.
Answer framework
For any Derivatives item set, use these steps to find the answer the exam expects.
- For forward commitments, compute the no-arbitrage price at inception (spot compounded at the risk-free rate, adjusted for carry), remembering the value is zero at inception.
- Value an existing forward or swap over its life as the spot and rates change.
- For options, apply the value drivers (volatility and time raise value) and put-call parity (call plus bond equals put plus underlying) to find a missing price.
- Value an option with the binomial model by building the tree, computing payoffs, and discounting with risk-neutral probabilities at the risk-free rate.
- Pull the right figures from the vignette and compute precisely, since no-arbitrage pricing is exact. Where two approaches seem to fit, choose the no-arbitrage method the question specifies.
Practice question
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Study strategy
Approach Level 2 Derivatives as precise, no-arbitrage pricing, where the vignette format rewards exact computation. Start with forward commitments: compute the no-arbitrage forward price (spot compounded at the risk-free rate, adjusted for carry), and firmly separate the price (set at inception, with zero value) from the value (changing over the contract's life). Learn swap pricing and valuation the same way.
Then master option valuation: the value drivers (volatility and time raise value), put-call parity (and its exact arrangement of call, put, underlying and bond), and especially the binomial model, building the tree and discounting with risk-neutral probabilities at the risk-free rate, never real-world probabilities.
Because the calculations are exact and tested in vignettes, drill binomial-tree and forward-valuation item sets, practicing careful input selection and computation. Because Level 2 is tested through vignettes, practice full item sets under timed conditions (about 12 minutes per set), pulling the right figure from the right exhibit, and review misses by checking both input selection and calculation. Afterwards, move to Alternative Investments.
FAQ
How much of CFA Level 2 is Derivatives?
Derivatives is 5-10% of the exam, a smaller weight, but its no-arbitrage pricing is exact and unforgiving in the vignette format, and it connects to fixed income and portfolio management.
What is the difference between the price and the value of a forward?
The forward price is set at inception by no-arbitrage so the contract has zero value to both parties. The forward value is the contract's worth during its life, which changes as the underlying's spot price and interest rates move away from the locked-in forward price.
Why does a fair forward have zero value at inception?
Because the forward price is set precisely so that no party can earn a riskless profit and no premium changes hands. With the price fair, the expected gains and losses offset, so the contract is worth zero to both parties at the moment it is initiated.
What is put-call parity?
A no-arbitrage relationship for European options stating that a call plus a risk-free bond (equal to the present value of the strike) equals a put plus the underlying asset, for the same strike and maturity. It lets you solve for a missing instrument's price from the other three.
How does the binomial model value an option?
It builds a tree of the underlying's possible up and down moves, computes the option's payoff at each final node, and discounts those payoffs back to the present using risk-neutral probabilities and the risk-free rate. This no-arbitrage approach extends to multiple periods.
Why use risk-neutral probabilities instead of real ones?
No-arbitrage option valuation discounts expected payoffs computed with risk-neutral probabilities at the risk-free rate, because this replicates the option's payoff with a portfolio of the underlying and the risk-free asset. Using real-world probabilities would require a risk-adjusted discount rate that is not needed in this framework.
How does Derivatives connect to the rest of the Level 2 exam?
Derivatives pricing relies on the term structure and interest rate models from fixed income, and derivatives are used to hedge and manage risk in portfolio management, while the no-arbitrage reasoning is a theme throughout valuation.
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