Options Trading Glossary

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Curated definitions of the core options trading terms: Greeks, IV concepts, dealer-flow metrics, and structural language. Each entry links to live data or the relevant deep-dive. For longer-form treatments, browse the Charts & Analytics docs.

0DTE Options (Zero-DTE, 0-DTE)
Options expiring on the same trading day they are traded. Gamma and theta are extreme: an ATM 0DTE option can move from 0 to fully ITM in minutes, and time decay collapses the premium hour by hour. Liquidity is concentrated in SPX/SPY/QQQ; single-stock 0DTE is rare except on weekly cycles. Dealer hedging on 0DTE chains drives much of late-session intraday volatility.

0DTE Options Docs

American Exercise
An exercise style that allows the option holder to exercise at any time up to and including expiration. Most listed equity options are American style. The early-exercise premium is small for non-dividend stocks but becomes material on calls right before ex-dividend dates and on deep ITM puts. Pricing American options requires Binomial trees, PDEs, or Longstaff-Schwartz Monte Carlo because the early-exercise boundary has no closed-form Black-Scholes solution.

Binomial Tree Docs

At-the-Money (ATM) (ATM)
An option whose strike is equal to (or very close to) the current underlying spot price. ATM options have the highest gamma and vega, making them the most sensitive to spot and IV moves. Delta is roughly 0.50 for calls and -0.50 for puts. The ATM straddle (long ATM call + long ATM put) is the canonical reference for the market-implied expected move.

Expected Move

Bates Model
A pricing model that combines Heston stochastic volatility with Merton-style log-normal jumps. Captures both smooth volatility dynamics (smile, skew, term structure) and discontinuous price moves simultaneously. The most expressive of the standard calibration set; when Bates significantly outperforms Heston alone in fit quality, it confirms the market is pricing in jump risk. Calibration is slow because the parameter space is larger than Heston or Merton alone.

Jump Diffusion Docs

Binomial Tree
A discrete-time pricing method that models the underlying as moving up or down by fixed factors at each node, then walks back through the tree to value the option at each step. Cox-Ross-Rubinstein is the canonical version. Binomial pricing is the standard tool for American options because the early-exercise condition can be checked at every node. As steps grow large, the tree converges to Black-Scholes for European options.

Binomial Tree Docs

Black-Scholes Model (BSM, Black-Scholes-Merton)
The closed-form European-option pricing model published by Black, Scholes, and Merton in 1973. Assumes geometric Brownian motion with constant volatility, no jumps, frictionless markets, and continuous trading. Despite the unrealistic assumptions, Black-Scholes remains the universal reference: every other model is calibrated and compared back to it, and implied volatility is defined by inverting Black-Scholes from observed prices.

Black-Scholes Docs

Break-Even Price
The underlying price at which an options position has zero profit or loss at expiration. For a long call it is strike + premium; for a long put it is strike - premium. Multi-leg structures have two break-evens (iron condors, straddles). Break-evens are expiration-only values; the mark-to-market P/L mid-trade depends on time value and IV.

Break-Even Calculator

Butterfly Spread
A three-strike, four-leg structure: long one ITM, short two ATM, long one OTM (long-call butterfly). Maximum profit at the middle strike at expiration; defined risk on both wings. A pin trade: profitable when the underlying expires near the middle strike with low realized volatility. Iron butterflies are the credit-spread equivalent (short ATM straddle wrapped in a long strangle).

Butterfly Strategy

Calendar Spread (Time Spread, Horizontal Spread)
A position that sells a near-dated option and buys a longer-dated option at the same strike. Long vega and long theta in normal term-structure conditions; profits from term-structure normalization (front IV collapsing relative to back IV) and from the underlying staying near the strike. The classic post-earnings trade: short the high-IV front-month, long the lower-IV back-month, capture the IV-crush spread.

Calendar Spread Strategy

Calibration
The process of fitting a pricing model's parameters to observed market option prices (or implied volatilities) by minimizing a fit error. For Heston, this means finding rho, kappa, theta, sigma_v, and v0 that reproduce the observed surface. Calibration quality is measured by IV RMSE; a clean fit is below 0.5%, a poor fit above 2%. Cross-model RMSE comparison is a regime signal: when smooth-vol models stop fitting well, the market is pricing something they cannot capture.

Calibration Docs

Cash-Secured Put (CSP)
A short put fully collateralized by cash equal to the strike multiplied by 100 multiplied by the contract count. The trader either keeps the premium if the put expires OTM or buys the stock at the strike (effective price = strike - premium received) if assigned. Common income strategy on stocks the trader is willing to own; risk profile is identical to a covered call on the same stock at the same strike (synthetic equivalence).

Cash-Secured Put Strategy

Charm (Delta Decay, DdeltaDtime)
The rate of change of delta with respect to time, measuring how quickly delta drifts as expiration approaches. ATM charm is small; OTM and ITM charm grow with time-to-expiry compression. Charm flow is a documented late-day phenomenon: dealer delta-hedging needs change predictably as time decays, producing recurring patterns in spot tape on options-expiration days.

Charm Greek Docs

Charm Flow
The dealer hedging activity caused by charm-induced delta drift, particularly observable in the final hour of trading on OPEX Fridays. Calls and puts with similar moneyness have charms that flow opposite directions, so the net depends on the imbalance of dealer call-vs-put exposure. Charm flow is part of the structural explanation for the "afternoon drift" patterns near expiration.

Charm Flow Docs

Collar
A position combining long stock with a long OTM put (downside protection) and a short OTM call (financing). The put establishes a floor; the call caps upside. Zero-cost or low-cost when strikes are chosen so put premium equals call premium. Common strategy for protecting an appreciated long-stock position without selling and triggering taxes.

Collar Strategy

Color (DgammaDtime)
The rate of change of gamma with respect to time. Higher-order Greek that becomes meaningful for short-dated options where gamma is rapidly compressing or expanding. Most useful for understanding why ATM gamma explodes in the final week before expiration even though spot has not moved.

Color Greek Docs

Convexity
The non-linear (curved) component of an option's P/L profile relative to spot. Long options are positively convex (they gain more on big up-moves than they lose on big down-moves). Convexity is the underlying mechanism that makes long options superior to linear positions for capturing fat-tailed outcomes. Gamma is the local measure of convexity.

Convexity Docs

Covered Call
Long 100 shares plus 1 short OTM call against them. Income strategy: collect premium in exchange for capping upside above the strike. Synthetically equivalent to a cash-secured put at the same strike. Best results in flat-to-mildly-bullish markets with elevated IV; underperforms outright stock in strong rallies and offers limited downside protection in selloffs.

Covered Call Strategy

Dealer Delta Exposure (DEX) (DEX)
The aggregate delta exposure dealers carry as the counterparty to retail and institutional flow. Negative net DEX means dealers are short-call-heavy (and therefore hedged long stock); positive net DEX means dealers are short-put-heavy (and therefore hedged short stock). DEX changes as flow comes in, and the resulting hedge adjustments contribute to the bid-side / offer-side flow that influences intraday spot tape.

Dealer Delta Exposure Docs · DEX Leaders

Delta
The sensitivity of option price to a $1 change in the underlying. This is the first-order directional Greek. Long calls have delta in [0, 1]; long puts in [-1, 0]. At-the-money deltas are roughly 0.50 / -0.50 and drift toward 1 / -1 as options move ITM. Delta doubles as the risk-neutral probability the option expires ITM (approximately, under Black-Scholes). Aggregate portfolio delta is what dealers hedge to stay flat.

Greeks Reference

Delta Hedging
Continuously adjusting a share position to offset the delta of an options position, keeping the combined portfolio delta-neutral. Dealers hedge aggregate short-options positions this way. This is the mechanism that produces the gamma exposure (GEX) regime effects described on per-ticker pages. In positive gamma, hedging sells rallies and buys dips (vol-dampening); in negative gamma, it amplifies moves.

Gamma Exposure (GEX) · SPY GEX

eSSVI (Extended Surface SVI)
A volatility-surface parameterization that fits an entire (strike x expiry) IV surface simultaneously, rather than per-expiry slices. Requires at least 30 IV points across at least 3 tenors. Reports IV RMSE only (no price RMSE) since it parameterizes the surface directly. eSSVI is the workhorse for full-surface calibration in the Bates/Heston/SABR ensemble.

eSSVI Docs

European Exercise
An exercise style that only allows the option holder to exercise at expiration. Index options on SPX, NDX, RUT are European; equity options are typically American. European pricing is what Black-Scholes solves directly; American pricing requires numerical methods (binomial, PDE, LSM Monte Carlo). The pricing gap between American and European on the same underlying is the early-exercise premium.

Black-Scholes Docs

Expected Move
The 1-standard-deviation implied price range a given expiration is pricing into the underlying. Computed either as sigma * S * sqrt(T) (IV method) or approximately 1.25 * the ATM straddle (Brenner-Subrahmanyam identity). The 1-sigma bracket carries roughly 68% implied probability; the 2-sigma bracket about 95%. Real returns are fat-tailed, so both ranges understate extreme outcomes.

Expected Move Docs · Calculator

Fail-to-Deliver (FTD) (FTD)
A settlement failure where shares were sold but not delivered to the buyer within the standard settlement cycle (currently T+1 for US equities since May 28, 2024; previously T+2). SEC publishes FTD data semi-monthly. Persistent FTDs on a security can indicate hard-to-borrow constraints, naked short selling, or operational issues, and securities with large FTDs may be added to the Reg SHO threshold list, restricting further short sales.

Fail-to-Deliver Docs

FFT Pricing (Fast Fourier Transform)
A numerical option-pricing method that uses the characteristic function of the underlying return distribution rather than direct simulation or analytic formulas. Once the characteristic function is known (Heston, Variance Gamma, Bates, Kou, Merton all have closed-form characteristic functions), pricing every strike on a chain is a single Fourier transform. FFT is the engine behind millisecond-latency full-chain scanning.

FFT Docs

Gamma
The rate of change of delta with respect to spot, the second-order directional Greek. Long options are long gamma; short options are short gamma. ATM options near expiration have the highest gamma, which is why expiration-week hedging flows are so explosive. Positive gamma (long) gains delta in a rally and loses delta in a drop; negative gamma (short) does the opposite and requires buying high / selling low to stay hedged.

Gamma Exposure (GEX)

Gamma Exposure (GEX) (GEX, Dealer Gamma)
The total dollar-delta change dealers must hedge per 1% move in the underlying, under the standard assumption that retail is net long calls and net short puts. Positive GEX damps volatility (dealers buy dips, sell rallies); negative GEX amplifies it (dealers chase moves). GEX is a chain-level aggregate, so concentrations at specific strikes produce "call walls" and "put walls" that act as support/resistance.

GEX Docs · GEX Leaders

Gamma Flip (Gamma Flip Point, Zero Gamma Level)
The spot price at which net dealer gamma changes sign from positive to negative (or vice versa). The gamma flip is the most actionable level on a GEX chart: above the flip, dealer hedging dampens volatility; below the flip, dealer hedging amplifies it. Persistent breaks below the gamma-flip level on indices are empirically associated with regime transitions to higher realized volatility.

GEX Docs

Gamma Squeeze
A self-reinforcing rally driven by dealer hedge-buying of the underlying. As retail concentrates call buying near current spot, dealers fill the short-call side and accumulate negative-gamma exposure; to stay delta-neutral they buy the underlying, which pushes spot higher, which pushes more calls ITM, which forces more dealer stock-buying. The 2021 GME and AMC moves are the canonical examples. Gamma squeezes only sustain while flow concentration persists.

Gamma Squeeze Docs

Heston Model
A stochastic-volatility model published by Steven Heston in 1993. Variance follows a mean-reverting process correlated with spot, which captures the volatility smile through correlation (rho) and vol-of-vol (sigma_v). Heston is the workhorse for surface-aware pricing; calibrated Heston Greeks are the standard for vol-arbitrage applications. Limitations: Heston cannot capture jumps without a Bates extension.

Heston Model Docs

Historical Volatility (HV) (HV, Realized Volatility, RV)
The annualized standard deviation of historical log returns over a rolling window (commonly 20 or 30 trading days). HV is backward-looking and measures what actually happened; IV is forward-looking and prices what the market expects. The IV/HV spread (IV minus HV) is the volatility risk premium; the IV/HV ratio is a richness signal for premium-selling decisions.

IV vs HV History

Implied Volatility (IV) (IV)
The volatility input that makes a pricing model (usually Black-Scholes) match the observed market option price. IV is forward-looking and reflects the market's priced-in expectation of future volatility plus a risk premium. Different strikes and expirations have different IVs (producing the volatility smile/skew). Real-time IV depends on the quote source and solver conventions; mid-of-bid-ask is the industry default.

IV vs HV History · IV Calculator

Iron Condor
A four-leg credit-spread structure: short OTM put + long further-OTM put + short OTM call + long further-OTM call. Defined-risk neutral position; profits if the underlying stays between the short strikes through expiration. Premium-selling income strategy with capped loss equal to the wing width minus the credit received. Best in high-IV-rank, low-vol-of-vol environments.

Iron Condor Strategy

IV Crush
The sharp drop in implied volatility immediately following a scheduled event (earnings, FDA, FOMC) as the event-premium priced into options collapses. A stock can move in your expected direction but still produce a losing long-options trade because the IV decline overwhelms the realized-move gain. This is why directional event trades are often better expressed through spreads or calendars than outright long options.

Biggest IV Change Screener

IV Percentile
The percentage of trading days over a lookback window (usually 252 days) on which IV was below the current level. Above 80 indicates IV is in the top 20% of recent readings. More stable than IV Rank when the IV history has occasional outliers, because IV Percentile counts days rather than positioning within a min-max range.

High IV Rank Screener

IV Rank
Where current implied volatility sits within its 52-week range, scaled 0-100. IV Rank of 80 means today's IV is in the top 20% of the past year's readings. Above 50 is generally considered elevated; above 70 is typical for premium-selling setups. More sensitive to outliers than IV Percentile, which counts days below today's level instead of min-max positioning.

High IV Rank Screener

Jump Diffusion
A class of pricing models that adds discontinuous price jumps to standard diffusion dynamics. Merton (1976) uses log-normally distributed jumps at a Poisson arrival rate; Kou (2002) uses double-exponential jump sizes; Bates (1996) combines Heston stochastic volatility with Merton jumps. Jump models price tail risk and event premium that smooth-vol models cannot capture; calibrated jump intensity is a regime indicator.

Jump Diffusion Docs

Local Volatility (Dupire Model)
A pricing model that calibrates a deterministic volatility function sigma(S, t) to fit the observed implied-volatility surface exactly. Dupire (1994) derived the formula. Local volatility produces internally consistent prices for vanilla options but tends to underestimate forward skew, which is why stochastic-volatility models often outperform it on path-dependent products. eSSVI is a common parameterization for the input surface.

Local Volatility Docs

Max Pain
The strike at which the aggregate dollar value of all outstanding options contracts would expire with the least total intrinsic value, the price where option writers collectively lose the least. The concept describes a gravitational pull that dealer hedging flows can create around high-OI strikes near expiration, not a deterministic forecast. Effect is strongest on high-OI index ETFs in the final days before expiry.

Max Pain Docs · SPY Max Pain

Moneyness
A measure of how far an option is from being at-the-money, expressed either as the strike-to-spot ratio (K/S), the log-moneyness ln(K/S), or the standardized moneyness ln(K/S) / (sigma * sqrt(T)). Standardized moneyness is the most useful measure across expirations because it normalizes for time-to-expiry. ITM, ATM, and OTM are the categorical version of the same concept.

Volatility Surface Docs

Monte Carlo Pricing
A pricing method that simulates thousands or millions of price paths under a model's risk-neutral dynamics, computes the option payoff on each path, and discounts the average back to present. Monte Carlo handles path-dependent options (Asian, Lookback, Barrier) that have no closed-form solution. Convergence is slow (error scales as 1/sqrt(N)), so variance-reduction techniques and GPU acceleration are common.

Monte Carlo Docs

Negative Gamma
A regime in which net dealer gamma exposure is negative. Dealer hedging amplifies moves: they buy strength and sell weakness to stay delta-neutral, which feeds the move. Realized volatility tends to expand and trends accelerate. Persistent negative-gamma regimes coincide with elevated VIX and steep put skew. The gamma flip is the boundary between negative and positive regimes.

Negative Gamma Docs

Open Interest (OI) (OI)
Total number of outstanding option contracts that have not yet been closed, exercised, or expired. OI accumulates across sessions (unlike volume, which resets daily) and reflects institutional positioning that has been built up over time. High OI concentrations create hedging walls and influence dealer gamma exposure. OI is reported one day in arrears.

Open Interest Docs · Highest OI Screener

PDE Pricing (Partial Differential Equation Pricing)
A numerical pricing method that solves the option-valuation PDE (Black-Scholes PDE in the simplest case) on a discretized grid of spot and time. PDE methods are the standard for American options and for path-dependent payoffs that admit a PDE formulation. Implicit and Crank-Nicolson schemes are the workhorses; the adjoint method computes all Greeks in a single forward+backward pass.

PDE Pricing Docs

Pin Risk
The risk that the underlying closes almost exactly at a short-option strike at expiration, creating assignment uncertainty. You don't know until after the close whether the option finished slightly ITM (auto-exercised) or slightly OTM (expired worthless). Stocks at high-OI strikes often do pin, with max-pain and GEX walls the structural drivers.

Max Pain & Pinning

Positive Gamma
A regime in which net dealer gamma exposure is positive. Dealer hedging dampens moves: they sell rallies and buy dips to stay delta-neutral, which mean-reverts spot. Realized volatility tends to compress and price pins to high-gamma strikes. Most trading days in normal-vol environments are positive-gamma regimes; transitions to negative gamma typically coincide with volatility events.

Positive Gamma Docs

Probability of Profit (POP) (POP)
The market-implied probability that a position will close profitable at expiration, computed by integrating the risk-neutral density over the profitable range. POP is risk-neutral, so it incorporates the market's risk-premium and for options selling typically overstates the real-world probability. A common sanity check is comparing it to the simpler delta-based approximation for the short legs.

Probability Analysis

Rho
The sensitivity of option price to a 1-percentage-point change in the risk-free rate. Calls have positive rho; puts have negative rho. Rho is small for short-dated options (weeks/months) but becomes material for LEAPS and long-dated structures. Rho also matters for term-structure trading when Fed policy expectations shift across the curve. Rate-cut pricing shows up in long-dated option values before it shows up in short-dated ones.

Greeks Reference

Risk Reversal
A position that buys an OTM call and sells an OTM put (or vice versa) at roughly equivalent deltas. Zero- or near-zero-cost; tracks skew directly. The 25-delta risk reversal is the industry-standard skew measure: its IV spread IS the 25-delta skew. Risk reversals are the cheapest way to express a directional view at the cost of undefined risk on one side.

Volatility Skew & Surface

Risk-Neutral Density (RND, Implied Density)
The probability density over future underlying prices implied by current option prices, derived via the Breeden-Litzenberger relation: the second strike-derivative of the call price (suitably discounted) equals the risk-neutral density at that strike. RND is what eSSVI Breeden-Litzenberger probability analysis computes. The risk-neutral measure differs from the real-world measure by the pricing kernel; the gap is the variance risk premium.

Risk-Neutral Density Docs

SABR Model (Stochastic Alpha Beta Rho)
A stochastic-volatility model published by Hagan-Kumar-Lesniewski-Woodward (2002). Captures volatility smile dynamics through the beta parameter (skew shape) and nu (vol-of-vol). SABR's closed-form approximations make it fast to calibrate per-expiration, which is why it became the standard in interest-rate derivatives and remains widely used for equity-options smile fitting.

SABR Model Docs

Short Interest
The number of shares sold short and not yet covered. FINRA reports short interest semi-monthly with a one-week lag. Short interest as a percentage of float is the key ratio: above 20% is high, above 40% is extreme and typically signals hard-to-borrow and elevated gamma-squeeze potential. Short interest combined with options positioning (high call OI on a high-SI name) is the canonical pre-squeeze signature.

Short Interest Docs

Short Volume
The portion of a security's daily trading volume that was sold short. FINRA publishes short-volume data daily for FINRA-regulated venues. Short volume captures market-making activity (which is typically delta-hedge-driven and not directional) as well as outright bearish flow. High short-volume ratios coupled with rising short interest are a more reliable bearish signal than either alone.

Short Volume Docs

Skew (Volatility Skew)
The variation of implied volatility across strikes at a fixed expiration. For equities, OTM puts trade at higher IV than OTM calls ("put skew") because of persistent demand for downside protection. The 25-delta skew (IV of 25-delta put minus IV of 25-delta call) is the standard measure. Steep skew = high crash-protection demand; flat/inverted skew is rare and usually short-lived.

Volatility Skew Docs · SPY Volatility

Speed (DgammaDspot)
The rate of change of gamma with respect to spot, the third-order directional Greek. Useful for understanding how quickly gamma will change as the underlying moves. Concentrated near ATM strikes for short-dated options. Practical applications are limited mostly to large books that need to manage the second-order risk in their gamma position.

Speed Greek Docs

Straddle
A long ATM call plus a long ATM put at the same strike and expiration. Pure long-volatility structure; profits from a large move in either direction. Maximum loss at the strike at expiration equals total premium paid. The ATM straddle price is the simplest market-implied expected-move signal: the straddle divided by sqrt(2/pi) approximately equals 1.25x the 1-sigma move.

Long Straddle Strategy

Strangle
An OTM call plus an OTM put at the same expiration, typically chosen at equal absolute deltas (e.g., the 25-delta strangle). Cheaper than a straddle because both legs are OTM, but the underlying must move further to be profitable. Short strangles are common premium-selling positions; long strangles are bets on large moves with lower entry cost than straddles.

Strangle Strategy

Term Structure
Implied volatility across expirations at fixed moneyness. Contango (far > near) is the normal state; backwardation (near > far) signals pricing-in of a near-term event like earnings or a Fed meeting. Term-structure inversions typically collapse quickly after the catalyst passes, and this is the core of calendar-spread trading.

Term Structure Docs

Theta
The sensitivity of option price to the passage of one day, the time-decay Greek. Long options have negative theta (they lose value every day); short options have positive theta. Theta is non-linear: it accelerates dramatically in the final weeks before expiration, especially for ATM options. Theta is the structural reason short-premium strategies (covered calls, CSPs, iron condors) have positive expected drift absent a large move.

Greeks Reference

Threshold List (Reg SHO Threshold List)
The list of securities that have had persistent fail-to-deliver positions for five consecutive settlement days, published daily under SEC Regulation SHO. Threshold-list securities are subject to additional short-sale restrictions: brokers must locate shares before short selling, and FTDs must be closed within 13 settlement days. Names appearing on the threshold list often have hard-to-borrow conditions affecting options pricing.

Fail-to-Deliver Docs

Vanna (DdeltaDvol)
The rate of change of delta with respect to implied volatility (or equivalently, vega with respect to spot). Vanna is concentrated at OTM strikes and matters during vol shifts: a rising IV environment makes OTM call deltas grow even without spot moving, forcing dealer hedge-buying. Vanna flow is part of the structural mechanism for vol-driven trend extensions.

Vanna Greek Docs

Variance Gamma (VG)
A pure-jump Levy process pricing model with three parameters: sigma (volatility), theta (skew), and nu (kurtosis). VG has no diffusion component; the entire return process is jumps with Variance-Gamma-distributed sizes. Fits well when the market is pricing fat tails and asymmetric returns; calibrated VG IV often differs from Heston in distinct ways that flag tail-pricing regimes.

Variance Gamma Docs

Vega
The sensitivity of option price to a 1-point (1%) change in implied volatility. Long options are long vega; short options are short vega. At-the-money options have the highest vega, and vega scales with sqrt(T) (time to expiration). Vega is what makes IV crush matter: long vega positions lose value when IV drops even if spot does not move.

Greeks Reference

Veta (DvegaDtime)
The rate of change of vega with respect to time. Most useful for understanding how quickly an options position's vol exposure decays as expiration approaches. ATM veta is small until the final weeks; far-OTM veta is small throughout. Long-dated options carry persistent vega exposure that veta tracks as the expiration window narrows.

Veta Greek Docs

VIX (CBOE Volatility Index)
The CBOE Volatility Index, a model-free 30-day expected volatility measure for the S&P 500 computed from a strip of SPX option prices. Often called "the fear gauge," VIX rises when SPX puts become expensive relative to calls (skew steepens) or when overall IV rises. VIX is itself optionable and futures-tradeable; VVIX measures the vol-of-VIX (the second-order fear gauge). See the CBOE VIX Methodology white paper for calculation details.

VIX Docs

Vol of Vol (VVIX)
The volatility of the VIX index itself, measured by VVIX (CBOE's 30-day vol-of-VIX index). Captures the market's pricing of how unstable the volatility surface is. Spikes in VVIX without a corresponding VIX spike are an early warning that the surface is becoming stress-prone; sustained low VVIX coincides with calm vol regimes. See the CBOE volatility-index methodology paper for the calculation details (covers VVIX alongside other broad-based volatility indices).

Vol of Vol Docs

Volatility Risk Premium (VRP) (VRP)
The empirical tendency for implied volatility to exceed subsequent realized volatility by a few vol points on average for indices and more for single stocks. VRP is the structural reason systematic premium-selling strategies (covered calls, iron condors, short strangles) have historically produced positive expected returns, though realized edge varies widely by regime, transaction costs, and tail-event sizing.

IV vs HV & VRP

Volatility Smile
A volatility-skew shape where both deep ITM and deep OTM options have higher IV than ATM, producing a U-shape across strikes. Common on currencies and on some equities; the equity-index norm is closer to a "smirk" (steep put-side skew, flat-to-falling call side). Stochastic-volatility and jump-diffusion models can both fit smiles, but they imply different out-of-sample behavior.

Volatility Smile Docs

Volatility Surface
The full 2D surface of implied volatility across strike and expiration. The surface combines the volatility skew (variation across strikes at a fixed expiration) and the term structure (variation across expirations at a fixed moneyness). eSSVI parameterizes the entire surface; per-slice methods like SABR fit each expiration independently. Surface stability is itself a regime indicator.

Volatility Surface Docs

Vomma (Volga, DvegaDvol)
The rate of change of vega with respect to implied volatility, the convexity of vega. Long OTM options have positive vomma; long ATM options have small or near-zero vomma (vega is at its peak there, so its derivative with respect to IV is small); short positions carry the opposite-sign vomma of the equivalent long. Vomma matters most for vol-arbitrage books that need to manage second-order vol risk and for understanding why deep OTM options gain value disproportionately in vol spikes.

Vomma Greek Docs

Zomma (DgammaDvol)
The rate of change of gamma with respect to implied volatility. A higher-order Greek that becomes meaningful when IV is shifting rapidly: gamma at OTM strikes can change materially as the surface re-prices. Zomma is mainly used in advanced risk-management contexts where the second-order gamma exposure to vol shifts must be tracked alongside vanna.

Zomma Greek Docs