Derivatives

How Perpetual Options Are Priced Without an Expiry Date Perpetual option pricing uses optimal stopping theory to derive a closed-form value where time decay is replaced by dividend yield and interest rate factors.

How Swaps Are Cleared Through a Central Counterparty How interest rate swaps are cleared through a CCP: the lifecycle from trade execution through counterparty substitution, daily margining, and default-fund contributions that mutualize risk.

How the Delivery Notice Process Works in Commodity Futures Step-by-step mechanics of delivery notice issuance by shorts, exchange matching, and physical or cash settlement in commodity futures contracts.

How the Fixed Rate on a Swap Is Calculated How swap dealers derive the at-market fixed rate using discount factors and forward rates, ensuring zero initial value.

How the Ratchet Mechanism Works in a Cliquet Option Understand cliquet options: how periodic returns are locked in, reset, and how the ratchet structure affects pricing and hedge costs.

How to Calculate the Cost of Unwinding a Swap Early Terminating a swap before maturity means paying or receiving mark-to-market breakage cost. Learn how fair value is calculated and why the cost can switch from negative to positive.

How to Read an Options Greeks Table Guide to interpreting delta, gamma, theta, vega, and rho columns in an options chain, sign conventions, and practical use.

Hull-White Model A one-factor short-rate model with mean reversion that fits the initial yield curve for pricing interest-rate derivatives.

Implied Volatility Implied volatility is the volatility level that makes the Black-Scholes model output equal to the market price of an option, representing the market's expectation of future price movement.

Implied Volatility in Options: What It Means for Premium Implied volatility reflects the market's forecast of future price swings embedded in option premiums. Learn how IV moves affect options even when stock prices stay flat.

Implied Volatility Rank and Its Effect on Vega How IV rank contextualizes vega exposure—why the same nominal vega means more or less depending on where IV sits relative to its historical range.

Implied Volatility vs Historical Volatility in Options How implied volatility reflects forward-looking market expectations of price swings while historical volatility measures realized past moves, and why the gap between them drives trading opportunity.

Implied Volatility vs Historical Volatility: Key Differences Implied volatility is what the market prices into options now; historical volatility is what the stock actually did. The gap reveals fear, opportunity, and model risk.

In-Arrears Swap A floating-rate swap where the reference rate is observed and fixed at the end of each accrual period, rather than at the beginning.

In-the-Money In-the-money describes an option that has positive intrinsic value because the underlying asset's price makes exercise immediately profitable.

In-The-Money Settlement Automatic or manual settlement of profitable options at expiration, by cash payment or stock delivery.

In-the-Money vs Out-of-the-Money Options In-the-money vs out-of-the-money options differ in intrinsic value, probability of profit, and premium. Understand moneyness and how it shapes option pricing and exercise.

Inflation Swap A swap that exchanges fixed interest payments for floating payments linked to inflation, used to hedge or speculate on inflation trends.

Initial Margin Initial margin is the upfront collateral deposit required to enter a futures contract, ensuring the trader has sufficient funds to cover potential losses.

Initial Margin Requirements for Swaps Initial margin for interest rate swaps is the cash buffer required at trade inception to cover potential mark-to-market losses. Learn SIMM, cleared vs. uncleared, and margin calls.

Installment Option An option purchased through a series of premium payments rather than a single upfront cost, spreading cost and risk over time.

Installment Options: How Staged Premium Payments Work Installment options let buyers pay premium in periodic installments, retaining the right to abandon at each payment date and lose only the paid amount.

Interest Rate Futures Exchange-traded derivatives on short-term interest rates or bond prices, used to hedge borrowing costs and interest-rate risk.

Interest Rate Option An option whose underlying is an interest rate or bond, used to hedge or speculate on changes in borrowing costs and bond prices.

Interest Rate Parity and the Forward Exchange Rate How interest rate parity determines the forward exchange rate and ensures arbitrage-free pricing between spot and future currency values.

Interest Rate Swap An interest rate swap is an agreement to exchange fixed interest payments for floating interest payments on a notional principal, enabling borrowers to change interest-rate exposure.

Interest Rate Swap Settlement Mechanics How interest rate swap settlement works: net cash flows, day-count conventions, fixing dates, and why only the difference is exchanged rather than notional amounts.

Interest Rate Swap: How the Fixed-for-Floating Exchange Works How interest rate swaps exchange fixed-rate and floating-rate payments, with a step-by-step example of cash flows and the economics driving both sides.

Interest Rate Swaps for Retirees and Pension Funds How pension funds and retirees use interest rate swaps to hedge long-dated liabilities and lock in predictable cash flows through receive-fixed agreements.

Interest Rate Swaps for Small Business Borrowers How small businesses use interest rate swaps to convert floating-rate loans to fixed rates, including minimum thresholds and termination costs.

Intrinsic Value Intrinsic value is the amount by which an option is in-the-money—the immediate profit if exercised—independent of any time premium.

Intrinsic Value vs Time Value in an Option Premium An option's price splits into intrinsic value (immediate exercise worth) and time value (remaining probability premium). Understanding this decomposition is key to pricing, risk, and trading strategy.

Iron Butterfly A four-leg option strategy combining a bull put spread and bear call spread with a shared center strike, designed for high-probability income in sideways markets.

Iron Condor A four-leg option strategy combining a bull put spread and bear call spread, designed to profit from stagnation and low volatility.

Iron Condor Adjustments When Price Breaks Out Defensive tactics to manage an iron condor when the underlying breaks past the short strike, including rolling, broken-wing conversion, and one-side closure.

Iron Condor vs Iron Butterfly: Key Differences Compare iron condor and iron butterfly risk/reward profiles, breakeven widths, and when each fits expected volatility.

ISDA Master Agreement The standard legal contract that governs bilateral over-the-counter derivatives transactions, setting default remedies, netting, and credit terms.

Jade Lizard An option strategy combining a short put with a short call spread such that the total premium collected exceeds the width of the call spread, eliminating downside risk.

Jump Spread A vertical spread strategy with wider-than-normal strike spacing, designed to reduce entry cost and increase profit potential at the expense of higher break-even requirements.

Jump-Diffusion Model Merton's extension of Black-Scholes that adds sudden discrete price jumps to capture fat-tailed return distributions.

Key Terms in a Futures Contract Specification Futures contract specs define contract size, grade, tick size, delivery terms, and trading rules. Learn what each field means and how they affect trading.

Knock-In Option A knock-in option is activated only when the underlying asset's price crosses a barrier level, making it cheaper than vanilla options due to lower exercise probability.

Knock-In vs Knock-Out Barrier Options: Key Differences Understand knock-in and knock-out barrier options: how activation barriers affect pricing, hedging cost, and downside protection in derivatives strategies.

Knock-Out Option A knock-out option terminates and becomes worthless if the underlying asset's price crosses a barrier level, making it cheaper than vanilla options.

Ladder Option Explained A ladder option locks in profits at preset price levels reached during the trade; each rung guarantees a minimum payoff once touched, unlike standard lookback or barrier options.

Lambda Percentage change in option value per percentage move in the underlying asset price.

LEAPS Options Long-term equity anticipation securities with expirations up to three years; equity options that blur the line between derivatives and straight equity positions.

Least-Squares Monte Carlo Longstaff-Schwartz regression method for valuing American and Bermudan options by estimating continuation value on simulated paths.

Leverage in Derivatives: How It Amplifies Gains and Losses How derivative contracts such as options and futures control large notional values with small margin or premium outlays, magnifying both upside and downside relative to owning the underlying asset directly.

Liability Swap A swap used by borrowers to convert the interest-rate exposure of an existing debt from fixed to floating or vice versa.

LIBOR Market Model A forward-rate framework for pricing caps, floors, and swaptions on LIBOR curves with direct market calibration.

Linear vs Non-Linear Derivatives: What the Difference Means for Risk Linear vs nonlinear derivatives: understand why futures move point-for-point with the underlying, while options have curved payoffs that create complex risk.

Local Volatility Model Dupire's framework that calibrates a deterministic volatility surface to fit all observed option prices exactly.

Long Call Butterfly vs Iron Butterfly Understand the cost, risk profile, and assignment mechanics of call-only butterflies versus iron butterflies for limited-risk directional trades.

Long Call Ladder A multi-leg option strategy that buys calls at multiple strikes, designed to profit from moderate moves while limiting cost through the sales of higher-strike calls.

Long Call vs Bull Call Spread: Cost and Upside Trade-Off A long call offers unlimited upside at a higher cost; a bull call spread caps upside but cuts the cost by half. Choose based on conviction and capital.

Long Combo A bullish options strategy combining a long OTM call with a short OTM put to create leveraged exposure with minimal net premium.

Long Option vs Short Option: Rights, Obligations, and Risk Long option vs short option: buyers hold rights with defined risk; writers assume obligations with unlimited loss. Covers P&L, margin, and Greeks.

Long Put Ladder A multi-leg option strategy that buys puts at multiple strikes, designed to profit from moderate declines while limiting cost through the sales of lower-strike puts.

Long Straddle An options strategy that buys both a call and put at the same strike and expiration, profiting from large moves in either direction while remaining neutral on direction.