CISI Derivatives (CISI) cheat sheet

A derivative is a contract whose value is derived from an underlying asset, rate, index or event; the four main families are futures/forwards, options, swaps and credit derivatives.

Exchange-traded products are standardised, cleared through a central counterparty (CCP) and marked to market daily; OTC products are bilaterally negotiated, customised and carry counterparty credit risk unless centrally cleared.

A CCP interposes itself between buyer and seller, becoming buyer to every seller and seller to every buyer; it mutualises default risk through margin, a default fund and a waterfall of loss-absorbing resources.

Initial margin covers potential future exposure over the close-out period; variation margin settles daily mark-to-market moves; the margin period of risk is typically 1 day for futures and longer (often 5 days) for cleared OTC positions.

Under EMIR-style regimes, standardised OTC derivatives must be centrally cleared, reported to a trade repository, and non-cleared trades attract bilateral margin; the clearing obligation applies to specified counterparty and product classes.

Payoff profiles: linear instruments (futures, forwards, swaps) have symmetric profit and loss; non-linear instruments (options) have asymmetric payoffs with capped loss for the buyer.

Cost-of-carry framework: fair forward price F = S x (1 + r)^T adjusted for carry income and storage, i.e. F = (S - PV(income) + PV(storage)) x (1 + r)^T.

Market participants: hedgers reduce existing risk, speculators take on risk for expected return, arbitrageurs exploit mispricing between related instruments, and market makers provide two-way liquidity.

Netting: payment netting settles only the net amount due; close-out netting converts all obligations into a single termination amount on default, which is enforceable only where legally recognised in the relevant jurisdiction.

A forward is an OTC agreement to buy or sell at a fixed price on a future date with no upfront payment; a future is an exchange-listed, standardised, margined equivalent with daily settlement.

Contango: futures price above the expected spot, typically when storage and financing costs exceed convenience yield; backwardation: futures below expected spot, typically when convenience yield exceeds carry costs.

Basis = spot price minus futures price; convergence to zero at expiry is enforced by the physical or cash-settlement mechanism of the contract.

Futures profit and loss per contract = (exit price - entry price) x contract multiplier x number of contracts, with long positions gaining when price rises and short positions gaining when price falls.

Hedging effectiveness is measured by the hedge ratio: minimum-variance hedge ratio = (standard deviation of spot changes / standard deviation of futures changes) x correlation between the two.

Marked to market: daily variation margin is credited or debited to the margin account; a fall below the maintenance margin triggers a margin call to restore the initial margin level.

A strip of futures or a forward rate agreement can lock in borrowing or lending rates; the effective locked rate equals the futures rate adjusted for the convexity effect in interest rate futures.

Cash-and-carry arbitrage: if F > S(1 + r)^T, buy the spot, borrow, sell the future and deliver at expiry; if F < S(1 + r)^T, reverse the trade by shorting the spot and buying the future.

Delivery and settlement: physically settled contracts require delivery of the underlying (or cheapest-to-deliver bond in bond futures); cash-settled contracts settle against an index or reference rate.

Call buyer: right, not obligation, to buy at the strike; maximum loss is the premium. Put buyer: right to sell at the strike; maximum loss is the premium. Writers receive premium and bear obligation risk.

Intrinsic value: call = max(S - K, 0); put = max(K - S, 0). Time value = option premium minus intrinsic value; time value decays to zero at expiry, fastest for at-the-money options in the final weeks.

Put-call parity (European, no dividends): C - P = S - K x e^(-rT). Violations create arbitrage via synthetic positions such as a protective put or covered call.

Black-Scholes inputs: spot price, strike, time to expiry, volatility, risk-free rate and dividend yield. Only volatility is unobservable, so implied volatility is backed out from the market price.

The Greeks: delta measures change in premium per unit change in spot; gamma measures change in delta; theta measures time decay; vega measures sensitivity to volatility; rho measures sensitivity to the risk-free rate.

Moneyness: in-the-money (call: S > K), at-the-money (S approximately K) and out-of-the-money (call: S < K); delta approximates the risk-neutral probability of finishing in the money.

Strategy payoffs: a long straddle profits from large moves in either direction; a covered call caps upside in exchange for premium; a protective put floors downside at the cost of the premium.

American options can be exercised at any time before expiry and are worth at least their intrinsic value; early exercise of a non-dividend-paying American call is generally not optimal.

Implied volatility rises with demand for options and around event dates; the volatility smile or skew shows that out-of-the-money puts often trade at higher implied volatility than at-the-money options.

An interest rate swap exchanges fixed for floating interest payments on a notional principal; the notional is not exchanged, so the swap's credit exposure is a small fraction of the notional.

Swap value = present value of the floating leg minus present value of the fixed leg (for a payer swap); at inception the fixed rate (the swap rate) is set so the value is zero.

Plain vanilla swap pricing uses the fixed rate that equates the present value of fixed leg cash flows to the present value of floating leg cash flows, discounted at the relevant curve.

A payer swap (pay fixed, receive floating) gains when rates rise; a receiver swap (receive fixed, pay floating) gains when rates fall.

Cross-currency swaps exchange principal and interest in two currencies; they carry both interest rate risk and foreign exchange risk, and the principal is typically exchanged at start and maturity.

Credit default swap (CDS): the protection buyer pays a periodic premium (spread) and receives a payout on a credit event; the spread widens as the reference entity's credit quality deteriorates.

Value at Risk (VaR) estimates the maximum loss over a given horizon at a given confidence level (e.g. 99% one-day VaR); it says nothing about the size of losses beyond that threshold.

Expected shortfall (CVaR) is the average loss conditional on exceeding the VaR threshold; it is a coherent risk measure and is preferred under Basel market risk standards.

Risk management controls: position and notional limits, stop-loss triggers, collateral and margin agreements (CSA), stress testing and scenario analysis, and independent valuation of complex derivatives.