Derivatives — Study Notes
CFA® Level I topic weight 5–8% · the smallest topic, with the most formula-friendly questions
Instruments & markets
- Forward commitments vs contingent claims: forwards, futures and swaps obligate both sides to transact at set terms; options give the buyer the right but not the obligation, in exchange for a premium. This one distinction sorts most classification questions.
- Forwards vs futures: forwards are customized, over-the-counter, settled at expiration, and carry counterparty risk; futures are standardized, exchange-traded, marked to market daily through a clearinghouse with margin requirements, which nearly eliminates counterparty risk.
- Swaps exchange series of cash flows — most commonly fixed for floating interest payments on a notional amount. A swap is economically a portfolio of forward agreements, one per settlement date, and has zero value to both sides at initiation.
- Why derivatives exist: risk transfer (hedging), price discovery, lower transaction costs, and leverage for expressing views. Criticisms center on leverage, complexity and systemic linkages — the exam expects both sides.
Pricing forward commitments
- No-arbitrage forward price: F₀ = S₀ × (1 + r)T for an asset with no carry cash flows — the cost of buying now and carrying to delivery. Benefits of holding (dividends, coupons, convenience yield) reduce the forward price; costs of carry (storage, insurance) raise it.
- Price vs value: the forward price is fixed at initiation so that the contract’s value starts at zero. As the spot price and time change, value accrues to one side: the long’s value = current spot − present value of the forward price.
- Futures equivalence: daily settlement resets futures value to zero every day; the accumulated gains/losses sit in the margin account rather than in contract value.
Options: moneyness, value & parity
- Moneyness: a call is in the money when S > X, a put when S < X. Intrinsic value is the exercise value (max(0, S − X) for calls; max(0, X − S) for puts); time value is premium minus intrinsic value and decays to zero at expiration.
- Value drivers: call value rises with the underlying price, time to expiration, volatility and the risk-free rate, and falls with the exercise price and expected dividends; put value moves opposite on price, exercise price, rate and dividends — but volatility raises both calls and puts.
- Put–call parity: S₀ + p₀ = c₀ + PV(X) — a protective put equals a fiduciary call. Rearranging replicates any leg synthetically (e.g., c₀ = S₀ + p₀ − PV(X)); violations imply arbitrage, and questions test spotting the rearrangement.
- European vs American: European options exercise only at expiration; American options any time. An American call on a non-dividend stock is worth no more than the European — early exercise sacrifices time value — while deep-in-the-money puts and dividend-paying underlyings can justify early exercise.
- One-period binomial valuation: build a riskless hedge of underlying and option, or equivalently weight the up and down payoffs with risk-neutral probabilities and discount at the risk-free rate. The real-world probability of the up move never enters — a deliberately counterintuitive point the exam loves.
Common traps
- Confusing forward price with forward value — the price is fixed at initiation; the value starts at zero and changes as spot moves.
- Thinking higher volatility hurts puts — volatility increases the value of both calls and puts.
- Using real-world probabilities in binomial pricing — valuation uses risk-neutral probabilities with risk-free discounting.
- Forgetting dividends in put–call parity and forward pricing — benefits of carry lower the forward price and shift parity by their present value.
- Treating futures like forwards for cash flow — daily marking to market creates interim cash flows a forward never has.
Drill 55 Derivatives practice questions
Pricing, parity and payoff drills with worked explanations, plus the topic’s share of a 540-question mock bank.
For exam preparation reference only — original condensed summaries of publicly known Level I curriculum concepts. Independent study aid. CFA Institute does not endorse, promote, or warrant the accuracy or quality of this product. CFA® and Chartered Financial Analyst® are registered trademarks owned by CFA Institute.
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