Derivatives

CFA® Level I, published weight 5–8%. Forwards, futures, swaps, options and arbitrage-free pricing.

What the outline covers

Derivative Instrument and Derivative Market Features
Forward Commitment and Contingent Claim Features and Instruments
Derivative Benefits, Risks, and Issuer and Investor Uses
Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives
Pricing and Valuation of Forward Contracts
Pricing and Valuation of Futures Contracts
Pricing and Valuation of Interest Rate and Other Swaps
Pricing and Valuation of Options
Option Replication Using Put–Call Parity
Valuing a Derivative Using a One-Period Binomial Model

Sample questions

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Question 1

A non-dividend-paying stock trades at $50. The one-year risk-free rate is 4%. The no-arbitrage one-year forward price is closest to:

S₀ = $50 · r = 4% · T = 1

A. $48.08
B. $50.00
C. $52.00
D. $54.00

Show the answer

C. F₀ = S₀(1 + r)ᵀ = 50 × 1.04 = $52.00. The expected future price of the stock is irrelevant to the forward price.

Reading: Derivatives — Arbitrage, Replication and the Cost of Carry, LOS 4.b

Question 2

According to put–call parity, a synthetic long call can be constructed from:

c + X/(1+r)ᵀ = p + S₀

A. Long put, long stock, short bond
B. Short put, long stock, long bond
C. Long put, short stock, long bond
D. Short put, short stock, short bond

Show the answer

A. Rearranging gives c = p + S₀ − X/(1+r)ᵀ: long put, long the underlying, and short a bond with face value equal to the strike.

Reading: Derivatives — Option Replication Using Put–Call Parity, LOS 9.a

Question 3

In a one-period binomial model with u = 1.25, d = 0.80 and a risk-free rate of 5%, the risk-neutral probability of an up move is closest to:

u = 1.25 · d = 0.80 · r = 5%

A. 0.44
B. 0.50
C. 0.56
D. 0.62

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C. π = (1 + r − d)/(u − d) = (1.05 − 0.80)/(1.25 − 0.80) = 0.25/0.45 = 0.556. The actual probability of an up move is not used.

Reading: Derivatives — Valuing a Derivative Using a One-Period Binomial Model, LOS 10.b

Question 4

At initiation, the value of a plain vanilla interest rate swap to the fixed-rate payer is:

A. Positive
B. Negative
C. Zero
D. Equal to the notional principal

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C. The fixed rate is set precisely so the present values of the two legs are equal, making the swap worth zero to both parties at inception.

Reading: Derivatives — Pricing and Valuation of Interest Rate Swaps, LOS 7.a

Question 5

Which of the following best describes the credit risk of an exchange-traded futures contract relative to an otherwise identical forward?

A. Higher, because of daily settlement
B. Lower, because of daily settlement and the clearinghouse
C. Identical, because the payoffs are identical
D. Undefined, because futures carry no credit risk at all

Show the answer

B. Daily mark-to-market settlement and the clearinghouse acting as counterparty substantially reduce credit risk relative to a bilateral forward.

Reading: Derivatives — Derivative Instrument and Market Features, LOS 1.c

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