CFA Derivatives Core Payoff Pricing Map

The Three-Part Derivatives Core

A derivative is a contract whose value depends on an underlying asset, rate, index, currency, commodity, or other reference variable. CFA questions often feel crowded because the same vignette can ask about contract type, payoff, value, profit, margin, or no-arbitrage pricing.

The clean path is to classify first.

flowchart TD A["Derivative contract"] --> B{"Right or obligation"} B -->|"Both parties obligated"| C["Forward or futures"] B -->|"Buyer has a right"| D["Option"] B -->|"Series of exchanges"| E["Swap"] C --> F["Map long and short payoff"] D --> G["Map intrinsic payoff and premium"] E --> H["Net fixed and floating legs"] F --> I["Apply pricing or value logic"] G --> I H --> I

That map prevents the most common exam mistake: reaching for a memorized formula before identifying what the contract actually requires.

Forwards: Customized Obligations

A forward contract is a private agreement to buy or sell an underlying at a set forward price on a future date. The long side agrees to buy the underlying. The short side agrees to deliver or sell it.

For a simple forward on one share with forward price 42, the long payoff at settlement is:

Long forward payoff = settlement spot price - forward price

If the underlying settles at 47, the long receives 47 - 42 = 5. If it settles at 38, the long has 38 - 42 = -4.

Forward Price Versus Forward Value

The forward price is the delivery price written into the contract. The value of the forward is what the contract is worth after market conditions change. At initiation, a fair forward often has value close to zero. Later, the contract can become positive to one party and negative to the other.

Example: Orchard Metals enters a six-month forward to buy copper at 9,000 per metric ton. One month later, new six-month-equivalent pricing for comparable copper exposure rises. The original long forward has gained value because it locks in a lower purchase price than the current market would require.

Futures: Standardized Obligations With Daily Settlement

A futures contract is similar in economic direction to a forward, but it is standardized and exchange-traded. The major operational difference is daily settlement: gains and losses are marked to market through the margin account each trading day.

That daily settlement can change the cash-flow timing even when the final payoff direction looks similar to a forward.

For exam purposes:

Long futures benefits when the futures price rises.
Short futures benefits when the futures price falls.
Daily settlement realizes gains and losses before final expiration.
Margin is collateral, not the purchase price of the underlying.

Options: Rights, Not Obligations

An option gives the buyer a right. A call gives the right to buy. A put gives the right to sell. The option buyer pays a premium for that right. The seller receives the premium and takes on the obligation if the buyer exercises.

For a call option with strike 50:

Call payoff at expiration = max(0, stock price - 50)

For a put option with strike 50:

Put payoff at expiration = max(0, 50 - stock price)

Payoff is not the same as profit. If a call costs 3 and expires with a payoff of 8, the buyer's profit is 5 before transaction costs. If the payoff is 0, the buyer loses the premium paid.

Swaps: Repeated Net Exchanges

A swap is a series of exchanges between two parties. The most common introductory example is an interest rate swap, where one side pays a fixed rate and receives a floating rate, while the other side does the opposite.

Suppose Lakefront Pension Fund enters a plain-vanilla interest rate swap with notional principal of 10,000,000. It pays fixed 4.20% and receives a floating rate. If the floating rate for the period is 4.75%, the net annualized rate difference in Lakefront's favor is 0.55%.

Approximate annualized net receipt = 10,000,000 x 0.0055 = 55,000

Actual swap settlement depends on the day-count and payment period, but the exam concept is the same: net the two legs rather than treating the notional as exchanged principal.

Payoff, Value, And Profit

These three words must stay separate.

Payoff

Payoff is the amount created by the contract's settlement rule at a point in time, often expiration. For a long call, payoff is intrinsic value at expiration.

Value

Value is what the contract is worth today. Before expiration, value can reflect time value, volatility, rates, and changes in the underlying.

Profit

Profit adjusts payoff or value for the initial cost, such as the premium paid for an option or transaction costs.

flowchart LR A["Contract terms"] --> B["Payoff rule"] B --> C["Current value"] C --> D["Profit after initial cost"] A --> E["Rights and obligations"] E --> B

The No-Arbitrage Pricing Lens

Derivatives pricing is not magic. In basic CFA problems, it often starts from no-arbitrage: equivalent economic exposures should not have inconsistent prices after financing, income, storage, or carry effects are considered.

For a simple forward on a non-income asset, the fair forward price is linked to spot price and financing cost. If the forward price is too high relative to spot-and-finance, arbitrageurs can buy the asset, finance it, and sell the forward. If the forward price is too low, the reverse cash-and-carry logic can appear.

The exact formula depends on the asset and assumptions. The exam habit is to first identify the carry components:

financing cost,
income or yield on the underlying,
storage cost for physical assets,
convenience yield for some commodities,
contract maturity.

Exam Framing

When a derivatives question starts to feel too large, reduce it to four checks:

Identify the contract type.
Label the long and short sides.
Draw or mentally map the payoff.
Decide whether the question asks for payoff, value, profit, or fair price.

That process works across forwards, futures, options, and swaps. It also keeps you from using an option premium in a payoff question, exchanging swap notional when only net interest is settled, or treating a futures margin deposit as the price of the underlying.