CFA® Level I Derivatives

The 10 learning modules

1. 01 Derivative Instrument and Derivative Market Features

   What a derivative is, the main types of underlying (equities, fixed income, currencies, commodities and credit) and the two ways contracts are traded. You compare customised over-the-counter contracts with standardised exchange-traded ones in terms of counterparty risk, transparency and liquidity, and learn what a central counterparty does.

   5 lessons in the Academy →

2. 02 Forward Commitment and Contingent Claim Features and Instruments

   The features of forwards, futures, swaps and options, and of credit derivatives such as credit default swaps. For futures you learn how margin and daily settlement work. The key distinction is between forward commitments, which oblige both sides to transact, and contingent claims, where one side has a right but not an obligation. Expect payoff and profit calculations for long and short positions.

   7 lessons · 6 videos in the Academy →

3. 03 Derivative Benefits, Risks, and Issuer and Investor Uses

   Why derivatives exist: they let users transfer risk, gain exposure cheaply, and trade with lower transaction costs and greater liquidity than in the underlying market. The module also covers their risks, such as leverage, basis risk, counterparty risk and systemic risk. You then see how issuers use derivatives to hedge commercial exposures (and how hedge accounting treats cash flow, fair value and net investment hedges) and how investors use them to change or replicate exposures.

   6 lessons in the Academy →

4. 04 Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

   The law of one price, how arbitrage enforces it, and how a derivative can be replicated by the underlying and borrowing or lending at the risk-free rate. Because a replicating position is riskless, the forward price does not depend on investors' risk preferences or the expected return of the underlying. It then adds the costs and benefits of holding the underlying: income, storage costs and convenience yield.

   6 lessons · 4 videos in the Academy →

5. 05 Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

   The difference between a forward's price, set at inception so that the contract has zero value, and its value, which changes as the spot price moves. You calculate forward prices with discrete and continuous compounding, value a forward during its life and at expiry, and price currency forwards. The second half covers interest rate forwards: implied forward rates from spot rates and forward rate agreements (FRAs), including their settlement.

   7 lessons · 4 videos in the Academy →

6. 06 Pricing and Valuation of Futures Contracts

   How futures pricing differs from forward pricing because of daily mark-to-market. The value of a futures position resets to zero at each settlement. Futures and forward prices are equal when interest rates are constant, but differ when futures prices are correlated with rates. You also work with interest rate futures on MRR, quoted as 100 minus the annualised rate, including basis point value and hedging.

   5 lessons · 2 videos in the Academy →

7. 07 Pricing and Valuation of Interest Rates and Other Swaps

   An interest rate swap viewed as a series of forward contracts with a single fixed rate. You calculate net periodic settlements, the swap rate from discount factors, and the value of an existing swap after rates have changed. The value is zero at inception for an at-market swap and becomes positive for the fixed-rate payer when market swap rates rise.

   6 lessons · 2 videos in the Academy →

8. 08 Pricing and Valuation of Options

   The building blocks of option value: exercise value, moneyness and time value, plus the no-arbitrage lower and upper bounds for European options. You replicate calls and puts with the underlying and a risk-free asset, and learn how option values change with the underlying price, the exercise price, time to expiration, the risk-free rate, volatility and income or costs of holding the underlying. Most questions test the direction of these effects.

   6 lessons · 2 videos in the Academy →

9. 09 Option Replication Using Put–Call Parity

   Put–call parity for European options, and how to use it to create synthetic calls, puts, underlyings and risk-free bonds, or to spot mispricing. The module extends this to put–call–forward parity, where a forward replaces the underlying. It also applies parity to a firm: equity as a call on its assets, risky debt as risk-free debt less a put.

   5 lessons · 2 videos in the Academy →

10. 10 Valuing a Derivative Using a One-Period Binomial Model

    Valuing an option when the underlying can move to one of two prices in a single period. You build a riskless hedge with the underlying and the option, which leads to the risk-neutral probability and the rule that a derivative's value is its expected payoff under that probability, discounted at the risk-free rate. Expect short calculations of call and put values and questions on why actual probabilities do not matter.

    6 lessons · 2 videos in the Academy →

What the questions cover

• Forward commitments vs contingent claims, and OTC vs exchange-traded markets and central clearing
• Benefits, risks and uses of derivatives for issuers and investors
• Arbitrage, replication and the cost of carry (income, storage costs and convenience yield)
• Pricing and valuing forwards, including FRAs, and futures with daily margining
• Interest rate swaps as a series of forwards: swap rate, periodic settlements and value
• Option exercise value, time value, lower bounds and the factors that drive option prices
• Put–call parity, put–call–forward parity and the one-period binomial model

Key formulas

Forward price with cost of carry (discrete)

$\displaystyle F_0(T) = \left[S_0 - PV_0(I) + PV_0(C)\right](1 + r)^T$I is income on the underlying (dividends, coupons) and C the carrying costs, such as storage. With neither, F = S × (1 + r)^T.Learn it: The cost of carry: income and costs of owning the underlying →

Forward price (continuous compounding)

$\displaystyle F_0(T) = S_0 e^{(r + c - y)T}$c is the storage cost rate and y the income or convenience yield. For an index, y is the dividend yield; for a currency, r and y are the price-currency and base-currency interest rates.Learn it: Commodities, convenience yield and carry by asset class →

Value of a long forward during its life

$\displaystyle V_t(T) = \left[S_t - PV_t(I) + PV_t(C)\right] - \frac{F_0(T)}{(1 + r)^{T - t}}$Only income and costs still to come count. At expiry this becomes S_T − F_0(T); the short's value is the negative.

Option exercise value

$\displaystyle c_T = \max(0, S_T - X), \quad p_T = \max(0, X - S_T)$Time value is the option price minus exercise value. Profit to the buyer subtracts the premium paid.

Lower bounds for European options

$\displaystyle c_0 \ge \max\left[0, S_0 - \frac{X}{(1 + r)^T}\right], \quad p_0 \ge \max\left[0, \frac{X}{(1 + r)^T} - S_0\right]$A price below the bound would allow arbitrage. For an out-of-the-money option the bound is zero.

Put–call parity

$\displaystyle S_0 + p_0 = c_0 + \frac{X}{(1 + r)^T}$A protective put equals a fiduciary call. Both options must be European, with the same underlying, exercise price and expiry.Learn it: Fiduciary call, protective put and put–call parity →

Put–call–forward parity

$\displaystyle \frac{F_0(T)}{(1 + r)^T} + p_0 = c_0 + \frac{X}{(1 + r)^T}$The present value of the forward price replaces the spot price. So c_0 − p_0 equals the present value of F_0(T) − X.Learn it: Put–call forward parity →

One-period binomial model

$\displaystyle \pi = \frac{1 + r - d}{u - d}, \quad c_0 = \frac{\pi c_u + (1 - \pi) c_d}{1 + r}$u and d are the up and down factors and r the risk-free rate per period. The same formula values a put with p_u and p_d.

Swap rate from discount factors

$\displaystyle s_N = \frac{1 - DF_N}{\sum_{i=1}^{N} DF_i}$An existing swap is worth (s_new − s_old) × ΣDF × notional to the fixed-rate payer, summing over the remaining periods.Learn it: Pricing a swap: the par swap rate →

The Derivatives formula sheet: the key formulas explained

Common mistakes

• Confusing a forward's price with its value. At inception the price is set so that the value is zero; afterwards the price stays fixed while the value moves with the underlying.
• Discounting the forward price over the full contract life instead of the remaining time (T − t) when valuing a forward during its life, or including income that has already been paid.
• Getting the sign of carry wrong. Income and convenience yield lower the forward price; storage costs raise it.
• Hedging a planned floating-rate borrowing with a long MRR futures position. Futures prices are 100 minus the rate, so they fall when rates rise; the hedge is a short futures position, which matches a long FRA.
• Using the MRR set at the end of a swap period for that period's floating payment. In a plain vanilla swap the rate is set at the start of the period and paid at the end.
• In the binomial model, weighting payoffs with the actual probabilities, or forgetting to discount the expected payoff at the risk-free rate.
• Assuming a longer time to expiration always raises option value. For a deep in-the-money European put it can lower it, because the holder waits longer to receive the exercise price.

How to study it

• Always ask whether a question wants the price or the value. The forward price is fixed at inception; the value starts at zero and moves with the underlying.
• Separate payoff from profit: profit subtracts the premium for the buyer and adds it for the seller.
• Learn put–call parity as two portfolios with the same payoff (a fiduciary call and a protective put). Every synthetic position and rearrangement then follows from moving terms across the equals sign.
• Draw a one-line timeline for every forward or swap question, marking today, the settlement dates and the remaining time. Most calculation errors come from discounting over the wrong period.
• Practise the binomial model until the risk-neutral probability and the discounting step take under a minute. The questions are short and reward a fixed routine.

Try 3 Derivatives questions

Practise and prove Derivatives

The question bank and the mock exams are the practice half of CheapMocks Academy. Try the free sample questions, see the topic weights for the whole exam and the latest Level I pass rates.

Derivatives FAQ