Derivative

A derivative's price is not an opinion about where the underlying is heading. It is set by the cost of building an equivalent position with cash instruments, because if the two differ a riskless arbitrage exists. For a forward on an asset with no cash flows, the no-arbitrage price is the spot price compounded at the risk-free rate to the settlement date. Where the underlying pays income or yields a benefit, that benefit is subtracted; where storage, insurance or financing costs arise, they are added. This is the cost-of-carry logic.

The same discipline extends to options, where the payoff is replicated by a position in the underlying financed by borrowing, rebalanced as the underlying moves. The practical consequence for a candidate is important: derivative valuation questions test relationships among spot, forward, carry and time, not directional forecasting skill.

Contracts split into two families by the shape of their payoff. Forward commitments (forwards, futures and swaps) lock both parties into a transaction, so gains to one side are losses to the other in equal measure. A long forward's value at expiration is simply the spot price minus the agreed forward price, positive or negative without limit.

Contingent claims (options and instruments containing embedded optionality) deliver a payoff only when a condition is satisfied. A call pays the excess of spot over the exercise price and nothing otherwise; the buyer's loss is capped at the premium while the writer's exposure is open-ended in exchange for that premium received up front. Credit default swaps behave as contingent claims because payment depends on a defined credit event. Recognising which family a contract belongs to determines whether the exposure is linear or truncated.

Futures and listed options trade on exchanges with standardised size, maturity and delivery terms. A central counterparty stands between buyer and seller, collects initial margin, and marks positions to market daily so that gains and losses settle in cash before they can accumulate. Default risk is mutualised and largely neutralised, but flexibility is sacrificed and margin calls create liquidity demands even on well-hedged positions.

Forwards and swaps are negotiated bilaterally, tailored to a specific exposure, notional and date. That customisation is why corporate hedgers use them, and why they carry counterparty credit risk. Post-crisis practice has narrowed the gap: much of the standardised swap market now clears centrally and is collateralised under master agreements. Candidates should be able to trace how clearing, margining and standardisation each reduce credit exposure while altering cash flow timing.

Derivatives appear wherever risk needs to be separated from ownership. Airlines and utilities hedge input costs, exporters hedge currency exposure, borrowers convert floating-rate debt to fixed with an interest rate swap, and portfolio managers adjust equity or duration exposure quickly using futures rather than trading a full basket of securities. Prices in these markets also serve as information: implied volatility, futures curves and swap rates reveal expectations that cash markets do not display directly.

On the balance sheet, derivatives sit at fair value as assets or liabilities, with notional amounts disclosed in the notes rather than recognised. A candidate should be able to distinguish notional from market value, identify the hedged risk, explain how leverage arises from a small initial outlay controlling a large exposure, and state which party bears which risk after the contract is struck.