Derivatives

Expiration vs Exercise in Derivatives: Key Differences The difference between letting a derivative expire and exercising it; when each applies and what determines the outcome.

Extendable Swap A swap contract where one party holds the right to extend the maturity beyond the original termination date, embedding a payer swaption.

Fence Strategy An options strategy combining long underlying, long at-the-money put, and short out-of-the-money call to define a bounded profit range while limiting losses.

Final Settlement The process at contract expiration when a futures or forward contract is resolved by cash payment or physical delivery—the final adjustment determining profit or loss.

Finite Difference Methods for Options Numerical PDE solvers—explicit, implicit, and Crank-Nicolson schemes—that discretise the Black-Scholes equation on a grid.

First Notice Day The earliest date on which the short in a physical futures contract may issue a delivery notice to the exchange.

Fixed-for-Floating Swap: Payment Mechanics Explained See exactly how net settlement payments are calculated in a fixed-for-floating swap, with a worked numerical example showing who pays whom.

Fixed-Strike vs Floating-Strike Lookback Options Understand the difference between fixed-strike and floating-strike lookback options, where the payoff depends on historical prices reached during the option's life.

FLEX Option An exchange-listed option contract allowing customization of strike, expiration, settlement method, and exercise style beyond standard terms.

FLEX Options Customisable options listed on exchanges where traders negotiate strikes, expirations, and settlement terms while retaining exchange clearing and transparency.

Forward Contract A forward contract is a customizable bilateral agreement to exchange an asset for cash at a fixed price on a future date, settled at maturity (not daily).

Forward Contract vs Futures Contract Forward and futures contracts both lock in future prices, but futures are standardized and marked-to-market daily, while forwards are bespoke and settled only at expiry.

Forward Contract vs Futures Contract: Key Differences Understand the core differences between forward contracts and futures contracts: standardization, settlement, counterparty risk, and mark-to-market mechanics.

Forward Curve The term structure of forward or futures prices across different delivery dates for a single commodity or financial asset.

Forward Measure A change of numeraire that uses a zero-coupon bond as the discount unit, simplifying interest-rate derivative pricing by eliminating the short-rate dynamics.

Forward Price Formula The no-arbitrage equation that determines a forward contract's price from the spot price, risk-free rate, carrying costs, and expected income.

Forward Rate Agreement An over-the-counter contract that locks in an interest rate for a future borrowing or lending period without exchanging principal.

Forward Rate Agreement Settlement Calculation How the cash settlement of an FRA is computed using the contract rate, reference rate, notional principal, and day-count convention.

Forward Start Option An option that is activated in the future with the strike price set at inception based on a predetermined formula.

Forward Start Option Explained How forward start options defer activation to a future date with the strike price set relative to spot, commonly used in employee compensation and structured products.

Forward Volatility and the Term Structure of Volatility How forward implied volatility is extracted from the volatility term structure to price and hedge options across different time horizons.

Forward-Start Options: Pricing and Use Cases How forward start option pricing works when the strike is set at a future date, using forward volatility and conditional pricing frameworks.

Forward-Starting Swap An interest-rate swap whose effective date begins in the future, allowing counterparties to lock in rates ahead of a known financing need.

Freight Rate Swap A derivative that locks in shipping costs by exchanging floating freight rates for fixed payments, used to hedge bulk cargo expense volatility.

Futures Basis: What It Is and Why It Changes Define basis as the difference between spot and futures prices, trace how it converges at delivery, and explain basis risk for hedgers.

Futures Commission Merchant A CFTC-registered intermediary that accepts customer orders and margin for futures and options trading, acting as a broker and custodian of collateral.

Futures Contract A futures contract is a standardized agreement to buy or sell an underlying asset at a fixed price on a specified future date, marked-to-market daily.

Futures Convergence The process by which a futures contract's price approaches the spot price as the expiration date nears.

Futures Margin Call Mechanics A futures margin call occurs when losses push an account below maintenance margin; brokers then demand cash or will liquidate positions.

Futures Margin vs Stock Margin: How Leverage Works Differently Why futures margin is a performance bond rather than a loan, and how leverage, interest, and margin calls differ fundamentally between futures and stock trading.

Futures Open Interest vs Volume Open interest measures outstanding contracts; volume measures daily trades. Together they reveal liquidity, participation, and whether positions are building or collapsing.

Futures Roll Cost Explained Futures roll cost is the economic gain or loss when closing a near-month contract and reopening in a later month. Learn how contango and backwardation affect roll costs.

Futures Roll Yield Futures roll yield is the gain or loss from rolling an expiring contract into the next maturity, separate from spot price movements.

Futures Strip A simultaneous position across consecutive delivery months of a futures contract, used to lock in average prices or hedge rolling exposures.

Gamma Gamma measures the rate at which an option's delta changes as the underlying asset price moves, quantifying the convexity and instability of option hedges.

Gamma Convexity The rate of change in delta as the underlying asset price moves, measuring an option's non-linearity and sensitivity to volatility changes.

Gamma Exposure: At-the-Money vs Out-of-the-Money Options Gamma at the money vs out of the money options: peaks at-the-money and declines sharply for strikes away from spot, creating different hedging burdens.

Gamma P&L: Realized vs Implied Volatility Gamma P&L arises when realized volatility exceeds implied volatility. Learn how long-gamma traders profit from daily rebalancing and delta hedging.

Gamma Risk in Options: Why It Matters Near Expiry Gamma risk in options: why delta changes faster near expiration, increasing hedging costs for options sellers and rebalancing risks for hedgers.

Gamma Risk Near Expiration Gamma risk in options accelerates near expiration as delta becomes more volatile. Learn why gamma spikes in final days and what it means for hedging.

Gamma Scalping A trading strategy that harvests profits from realized volatility by repeatedly delta-hedging a long-gamma position.

Gap Option An option contract where the strike determining exercise differs from the strike setting the payoff, creating a payout cliff.

Greeks Aggregation The process of summing and netting first- and second-order sensitivities across a multi-position options book to assess portfolio risk.

Greeks for Deep In-the-Money Options Deep in-the-money options have delta near 1, near-zero gamma and vega, and theta close to the risk-free rate. They behave like stock substitutes.

Greeks for Put Options Explained Greeks for put options show how delta, gamma, theta, and vega behave differently than calls; understand sign conventions and practical trading implications.

Hedging Effectiveness Ratio for Futures How the R-squared metric measures the fraction of spot price variance eliminated by a futures hedge and why it rarely reaches 100%.

Hedging with Futures Using futures contracts to transfer price risk to speculators—locking in costs or revenues and allowing businesses to focus on operations rather than market moves.

Heston Stochastic Volatility Model A pricing framework where volatility itself evolves randomly, allowing the model to capture the volatility smile observed in real option markets.

Historical Volatility Historical volatility measures past price movements as the standard deviation of returns over a lookback period, used to forecast future volatility for option pricing.

How an Interest Rate Swap Is Valued After Inception Learn how to value an interest rate swap mid-life using discounted cash flows as rates move, creating positive or negative mark-to-market after trade date.

How Discrete Dividends Affect Option Pricing How discrete dividend payments shift the forward price and fair value of calls and puts compared to continuous-yield models.

How Dividends Affect Call Option Prices Why expected dividends lower call option prices and raise put premiums; early exercise mechanics before ex-dividend dates.

How Futures Margin Is Calculated Learn how futures exchanges calculate initial and maintenance margin using SPAN and VAR models to cover counterparty risk.

How Implied Volatility Affects the Greeks A rise in implied volatility increases vega and gamma, compresses theta, and shifts delta for out-of-the-money options. Directional rules for vol-Greek relationships.

How Margin Works in Futures Contracts Step-by-step explanation of initial margin, variation margin, and margin calls in futures; the daily cash mechanics.

How Option Contract Size Changes After Stock Splits and Mergers Learn how option contracts adjust for stock splits, reverse splits, and mergers—what changes in strike price, deliverable shares, and contract multipliers.

How Option Strike Prices Are Set by Exchanges How option strike prices are set by exchanges using standardized intervals and adjustment rules that balance trader accessibility and liquidity.

How Options Are Priced: Intrinsic and Extrinsic Value How are options priced? The option premium equals intrinsic value (in-the-money gain) plus time value (extrinsic). Volatility, time, and rates determine the extrinsic component.

How Options Are Priced: The Black-Scholes Inputs Explained How spot price, strike, time to expiration, volatility, and interest rate move an option premium via Black-Scholes model intuition.

How Options Behave on Expiration Day What happens to option prices, liquidity, and assignment risk in the final hours before expiration, and key risks for position holders.