CFA Level 2 · Free topic practice

CFA Level 2 Derivatives: notes and free practice

CFA Level 2 Derivatives links no-arbitrage valuation to forwards, swaps and options. Read the contract and valuation date first, then calculate the position value and interpret how changing inputs affect it.

The key ideas, at a glance

Level 2 · Visual study guide Study illustration of an analyzed worksheet, calculator and checked answer.

Revalue the existing contract

Read the visual, then follow the worked example below. Use the stated case assumptions.

Illustrative worked case

Revalue the original delivery-price commitment

$ payoff per unit

48: -4
50: -2
52: 0
54: 2
56: 4
60: 8

The original delivery price is 52. At maturity with the share at 56, long payoff is 4. These points are expiration payoffs.

Key methods and mistakes for CFA Level 2 Derivatives
Concept	Rule or decision	Common mistake
Revalue the existing contract	No income: F0 = S0(1 + r)^T; long value = St - K / (1 + r)^(T-t)	A forward delivery price is not an upfront premium paid to enter a fair forward.
Price the contingent payoff	p* = (risk-free growth - down factor) / (up factor - down factor)	European put-call parity needs matching strikes, expiries and the stated income assumptions.
Scale and rebalance delta	Share-equivalent exposure = contracts × multiplier × option delta	A delta hedge does not remove volatility, jump, financing or all higher-order risks.
Solve the par fixed rate	Par rate = [1 - DF(T)] / Σ accrual × DF(payment date)	The par coupon is not simply the arithmetic mean of spot rates.

01Revalue the existing contract
No income: F0 = S0(1 + r)^T; long value = St - K / (1 + r)^(T-t)
Watch for: A forward delivery price is not an upfront premium paid to enter a fair forward.
02Price the contingent payoff
p* = (risk-free growth - down factor) / (up factor - down factor)
Watch for: European put-call parity needs matching strikes, expiries and the stated income assumptions.
03Scale and rebalance delta
Share-equivalent exposure = contracts × multiplier × option delta
Watch for: A delta hedge does not remove volatility, jump, financing or all higher-order risks.
04Solve the par fixed rate
Par rate = [1 - DF(T)] / Σ accrual × DF(payment date)
Watch for: The par coupon is not simply the arithmetic mean of spot rates.

Selected 2026 study concepts. Match your preparation to your registered exam-year curriculum. These notes are not complete curriculum coverage.

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Put the method to work

One worked example, from facts to answer

Given
Share 50, one-year rate 4%, no dividends; original delivery price 52.
Method
At maturity, if the share is 56, long payoff = 56 - 52.
Answer and interpretation
The payoff is 4; the original fair contract had zero value at initiation.

Original independent teaching example. Assumptions are stated above; this is not an official exam question or scoring key.

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10 free Derivatives questions

Five mini-cases, two questions each. Read the case facts, choose an answer and review the method. Short teaching cases, not complete exam item sets or a mock.

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Question 1 of 10Level II topic sample · Case 1 of 5DerivativesMultiple choice
Case facts
A non-dividend-paying share costs 80. The annual effective risk-free rate is 5%, and a one-year forward is initiated at its no-arbitrage delivery price. Six months later the share is worth 86, with half a year remaining and the same rate. Ignore costs and credit risk.
The original one-year forward’s no-arbitrage delivery price is:
Answer and explanations
With no dividends, F0 = 80 × 1.05 = 84.00; this is the delivery price, not an upfront payment.
Review the method
- A: 80 ignores the year of financing carry.
- B - correct: With no dividends, F0 = 80 × 1.05 = 84.00; this is the delivery price, not an upfront payment.
- C: 4 is the carry increment, not the full delivery price.
Question 2 of 10Level II topic sample · Case 1 of 5DerivativesMultiple choice
Case facts
A non-dividend-paying share costs 80. The annual effective risk-free rate is 5%, and a one-year forward is initiated at its no-arbitrage delivery price. Six months later the share is worth 86, with half a year remaining and the same rate. Ignore costs and credit risk.
Six months later, the existing long forward’s value is closest to:
Answer and explanations
86 - 84 / 1.05^0.5 = about 4.02 per share, discounting the remaining delivery payment.
Review the method
- A - correct: 86 - 84 / 1.05^0.5 = about 4.02 per share, discounting the remaining delivery payment.
- B: 2 subtracts the future payment without discounting the remaining half-year.
- C: 6 compares today’s share value with the original spot rather than the contract liability.
Question 3 of 10Level II topic sample · Case 2 of 5DerivativesMultiple choice
Case facts
A one-period binomial model starts with a share at 100. After one year it is either 120 or 80. The risk-free gross growth factor is 1.05. A European call has strike 100. No dividends, transaction costs or arbitrage opportunities are assumed.
The binomial model’s risk-neutral up-state probability is:
Answer and explanations
(1.05 - 0.80) / (1.20 - 0.80) = 0.625; it is a pricing weight.
Review the method
- A: Equal price jumps do not imply equal risk-neutral weights when the risk-free return is positive.
- B: 0.250 does not reproduce the risk-free expected growth factor.
- C - correct: (1.05 - 0.80) / (1.20 - 0.80) = 0.625; it is a pricing weight.
Question 4 of 10Level II topic sample · Case 2 of 5DerivativesMultiple choice
Case facts
A one-period binomial model starts with a share at 100. After one year it is either 120 or 80. The risk-free gross growth factor is 1.05. A European call has strike 100. No dividends, transaction costs or arbitrage opportunities are assumed.
The one-period binomial European call value is closest to:
Answer and explanations
[0.625 × 20 + 0.375 × 0] / 1.05 = about 11.90 today.
Review the method
- A: 12.50 is the risk-neutral expected payoff before discounting.
- B - correct: [0.625 × 20 + 0.375 × 0] / 1.05 = about 11.90 today.
- C: 20 is the up-state payoff, not the present value across states.
Question 5 of 10Level II topic sample · Case 3 of 5DerivativesMultiple choice
Case facts
A non-dividend-paying share is priced at 102. A European call with strike 100 and one year to maturity costs 7. Annual effective risk-free return is 5%. A put with identical strike and maturity is to be valued using put-call parity.
The parity-implied European put value is closest to:
Answer and explanations
Put = call + PV(strike) - share = 7 + 100 / 1.05 - 102 = about 0.24.
Review the method
- A - correct: Put = call + PV(strike) - share = 7 + 100 / 1.05 - 102 = about 0.24.
- B: 5 ignores discounting the strike payment.
- C: 9 reverses the share-versus-strike adjustment.
Question 6 of 10Level II topic sample · Case 3 of 5DerivativesMultiple choice
Case facts
A non-dividend-paying share is priced at 102. A European call with strike 100 and one year to maturity costs 7. Annual effective risk-free return is 5%. A put with identical strike and maturity is to be valued using put-call parity.
Which position replicates the call’s terminal payoff under the specified assumptions?
Answer and explanations
Rearranging parity gives call = stock + put - PV(strike); the borrowing is repaid at expiration.
Review the method
- A: A put alone pays in the opposite downside region.
- B: Short stock plus a put does not replicate the call’s upside payoff.
- C - correct: Rearranging parity gives call = stock + put - PV(strike); the borrowing is repaid at expiration.
Question 7 of 10Level II topic sample · Case 4 of 5DerivativesMultiple choice
Case facts
A dealer is short 200 call contracts, each representing 100 shares. Each call’s delta is 0.60 initially and becomes 0.65 after a small market move. The stock delta is one. Ignore contract rounding, costs and changes in contract count; hedge the position using shares.
To initially delta-hedge the dealer’s short calls, the required stock position is:
Answer and explanations
The calls have delta -200 × 100 × 0.60 = -12,000; buy 12,000 shares to offset it.
Review the method
- A: Short stock would add to the negative option delta.
- B - correct: The calls have delta -200 × 100 × 0.60 = -12,000; buy 12,000 shares to offset it.
- C: 120 ignores the 100-share contract multiplier.
Question 8 of 10Level II topic sample · Case 4 of 5DerivativesMultiple choice
Case facts
A dealer is short 200 call contracts, each representing 100 shares. Each call’s delta is 0.60 initially and becomes 0.65 after a small market move. The stock delta is one. Ignore contract rounding, costs and changes in contract count; hedge the position using shares.
When call delta rises to 0.65, the dealer should rebalance by:
Answer and explanations
Required stock rises to 200 × 100 × 0.65 = 13,000; add 1,000 shares to the original hedge.
Review the method
- A - correct: Required stock rises to 200 × 100 × 0.65 = 13,000; add 1,000 shares to the original hedge.
- B: Selling shares increases the now-negative net delta.
- C: Changing option delta means the earlier hedge no longer neutralizes the exposure.
Question 9 of 10Level II topic sample · Case 5 of 5DerivativesMultiple choice
Case facts
Annual discount factors at years 1, 2 and 3 are 0.96, 0.92 and 0.89. A plain three-year fixed-for-floating swap starts at par with annual payments and accrual factors of one. Use a single curve, no spread and no credit or funding adjustments; the floating leg resets at inception.
The three-year par fixed swap rate is closest to:
Answer and explanations
(1 - 0.89) / (0.96 + 0.92 + 0.89) = about 3.971% per year.
Review the method
- A: 11% is one minus the final discount factor before dividing by the annuity factor.
- B: 3.667% divides by three without discount-weighting payments.
- C - correct: (1 - 0.89) / (0.96 + 0.92 + 0.89) = about 3.971% per year.
Question 10 of 10Level II topic sample · Case 5 of 5DerivativesMultiple choice
Case facts
Annual discount factors at years 1, 2 and 3 are 0.96, 0.92 and 0.89. A plain three-year fixed-for-floating swap starts at par with annual payments and accrual factors of one. Use a single curve, no spread and no credit or funding adjustments; the floating leg resets at inception.
What is the swap’s inception value at the computed par rate under the case assumptions?
Answer and explanations
The par fixed rate equates fixed and floating leg present values, giving zero initial value under the stated assumptions.
Review the method
- A: Notional scales payments but is not the swap’s inception value.
- B - correct: The par fixed rate equates fixed and floating leg present values, giving zero initial value under the stated assumptions.
- C: A fair par swap does not grant one side a guaranteed positive initial value.

Four ideas to put to work

Find the method you need

Start with: Discount factors, long/short payoffs, probability weighting and per-share versus contract exposure.

METHOD 01

Revalue the existing contract

No income: F0 = S0(1 + r)^T; long value = St - K / (1 + r)^(T-t)

Set the original delivery price using the no-arbitrage carry relation.
Keep the old delivery price fixed when valuing an existing contract.
Discount the remaining contractual payment using the remaining time.

Worked example

Given: Share 50, one-year rate 4%, no dividends; original delivery price 52.
Calculate / decide: At maturity, if the share is 56, long payoff = 56 - 52.
Result: The payoff is 4; the original fair contract had zero value at initiation.

Watch for: A forward delivery price is not an upfront premium paid to enter a fair forward.

Practise this idea

METHOD 02

Price the contingent payoff

p* = (risk-free growth - down factor) / (up factor - down factor)

Calculate option payoffs in each terminal state.
Weight by risk-neutral probability and discount, not by a guessed physical probability.
For European options without dividends, use call + PV(strike) = put + share.

Worked example

Given: Share 100; up 130, down 90; risk-free growth 1.05; call strike 100.
Calculate / decide: p* = (1.05 - 0.90) / 0.40 = 0.375; call = 0.375 × 30 / 1.05.
Result: The one-period call value is about 10.71.

Watch for: European put-call parity needs matching strikes, expiries and the stated income assumptions.

Practise this idea

METHOD 03

Scale and rebalance delta

Share-equivalent exposure = contracts × multiplier × option delta

Include the sign of the option position and the contract multiplier.
Trade the opposite stock exposure to make initial delta approximately zero.
Rebalance when delta changes; gamma means the first hedge is not permanent.

Worked example

Given: Short 50 calls, 100 shares per contract, delta 0.40.
Calculate / decide: Option delta = -50 × 100 × 0.40 = -2,000 shares.
Result: Buy 2,000 shares for an initial delta-neutral hedge.

Watch for: A delta hedge does not remove volatility, jump, financing or all higher-order risks.

Practise this idea

METHOD 04

Solve the par fixed rate

Par rate = [1 - DF(T)] / Σ accrual × DF(payment date)

Use discount factors at the actual payment dates.
Include accrual fractions; they equal one only in the stated annual example.
At the par fixed rate, fixed and floating present values balance at inception.

Worked example

Given: Two annual discount factors: 0.95 and 0.90; accruals one.
Calculate / decide: Par rate = (1 - 0.90) / (0.95 + 0.90).
Result: The fixed rate is about 5.4054% in this single-curve example.

Watch for: The par coupon is not simply the arithmetic mean of spot rates.

Practise this idea

Questions about this topic

How does a forward price differ from the value of an existing forward?: The forward price is a delivery price for a newly specified contract under the model. An existing contract’s value depends on its agreed delivery price relative to current pricing and remaining timing.
Does a no-arbitrage value guarantee the realized payoff?: No. It is a pricing relationship under stated market and model assumptions. The realized payoff depends on the future outcome and contract terms.
Why can a hedge need rebalancing?: An exposure or sensitivity can change as prices, time and other inputs change. A contract size that matched the exposure initially may no longer match it later.

Apply the topic to a focused case

CFA Level 2 derivatives pricing sensitivities

Delta is a local sensitivity, so first specify whether it is quoted per option unit, share, contract or portfolio. Multiply by the small underlying-price move using matching units, then apply the contract multiplier and number of contracts if needed. A short position reverses the exposure. The delta-only estimate holds other inputs fixed and is an approximation rather than an exact new option price.

Case facts: A long option has delta 0.60 and gamma 0.08 per stated underlying-price unit. The underlying rises by 2; hold other inputs fixed and use the delta-gamma approximation.
Apply the method: Estimated value change = 0.60 × 2 + 0.5 × 0.08 × 2² = 1.20 + 0.16.
Interpretation: The estimated gain is 1.36 per option unit. Apply a contract multiplier separately; the 0.16 curvature term refines the delta-only estimate.

Work through the detailed application

Independent teaching cases under the stated assumptions, rather than official questions or scoring keys.

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One worked example, from facts to answer

Given

Method

Answer and interpretation

10 free Derivatives questions

The original one-year forward’s no-arbitrage delivery price is:

Six months later, the existing long forward’s value is closest to:

The binomial model’s risk-neutral up-state probability is:

The one-period binomial European call value is closest to:

The parity-implied European put value is closest to:

Which position replicates the call’s terminal payoff under the specified assumptions?

To initially delta-hedge the dealer’s short calls, the required stock position is:

When call delta rises to 0.65, the dealer should rebalance by:

The three-year par fixed swap rate is closest to:

What is the swap’s inception value at the computed par rate under the case assumptions?

Find the method you need

Revalue the existing contract

Worked example

Price the contingent payoff

Worked example

Scale and rebalance delta

Worked example

Solve the par fixed rate

Worked example

Questions about this topic

Apply the topic to a focused case

CFA Level 2 derivatives pricing sensitivities

Sources and curriculum scope