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Volatility & Greeks

Translate volatility and option sensitivities into practical expectations for price, time, and risk.
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50 terms

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A Three-Concept Reading Path

  1. 1Implied Volatility
  2. 2Delta
  3. 3Theta

Why this topic matters

Greeks describe how an option model responds when one input changes. Delta follows the underlying, gamma changes delta, theta tracks time passing, vega responds to implied volatility, and rho isolates interest-rate sensitivity.

Read price, time, and implied volatility together. Use delta to size directional exposure, gamma to track changing delta, theta to measure time decay, and vega to test a volatility move. Compare those inputs in the options calculator and choose the complete payoff that fits the setup.

Topic questions

Volatility & Greeks FAQ

B

5 terms

Bachelier Model

The Bachelier model is an option pricing model in which the underlying follows arithmetic Brownian motion, so price changes are normal and prices can fall below zero.

Backwardation

Backwardation is a futures curve shape in which a nearer contract trades above a later one, as when front-month VIX futures price above deferred months.

Binomial Option Pricing Model

The binomial option pricing model values an option on a tree of up and down price moves, working backward from expiration and testing exercise at each permitted node.

Black-76 Model

The Black-76 model is a formula that prices European options from the underlying forward or futures price, which already includes the cost of carry.

Black-Scholes Model

The Black-Scholes model is a formula that values a European-style option from the stock price, strike, time to expiration, interest rate, dividends and volatility.

C

4 terms

Cboe SKEW Index

The Cboe SKEW Index measures the skewness of 30-day S&P 500 returns implied by SPX options, scaled so 100 means zero skew and higher readings mean more negative skew.

Charm

Charm is the second-order option Greek that estimates how delta changes as time passes while the underlying price and other pricing inputs are held constant.

Color (Option Greek)

Color is the third-order option Greek that measures how fast gamma changes as time passes, showing whether a contract is building or bleeding convexity into expiration.

Contango

Contango is a futures curve shape in which later contracts trade above nearer ones, as when deferred VIX futures price above the front month.

D

3 terms

Delta

Delta is the first-order option Greek that estimates how much an option’s value changes for a one-unit move in the underlying, with other pricing inputs held constant.

Delta Neutral

Delta neutral describes a position whose combined delta is close to zero, so its value changes little for small moves in the underlying price.

Dispersion Trading

Dispersion trading is an options strategy whose classic long form sells index volatility and buys constituent-stock volatility, creating a short position in correlation.

E

2 terms

Earnings Volatility Cycle

The earnings volatility cycle is the recurring repricing of event premium before a company report and its removal or redistribution after results become known.

Expected Move

An expected move is an options-derived estimate of the magnitude, not the direction, of an underlying price change over a stated period.

G

3 terms

Gamma

Gamma is the second-order Greek that measures how fast an option’s delta changes for each one-point move in the underlying price.

Gamma Scalping

Gamma scalping is an options strategy that holds long-gamma options and repeatedly delta-hedges them with stock, using realized price swings to offset time decay.

Greeks P&L Attribution

Greeks P&L attribution decomposes an option position’s profit or loss into delta, gamma, theta, and vega contributions using a Taylor expansion of the pricing model.

H

1 term

Hedging

Hedging is the practice of adding an offsetting position to reduce the risk of an existing exposure, such as buying a put to limit losses on a stock holding.

I

5 terms

Implied Correlation

Implied correlation is the average correlation among an index’s constituent stocks implied by option prices, backed out from index and single-stock implied volatility.

Implied Volatility

Implied volatility (IV) is the annualized volatility that makes a pricing model reproduce an option’s market premium, showing how much movement the market prices.

Implied Volatility Crush

An implied volatility crush is a rapid decline in option-implied volatility, commonly after a scheduled event resolves uncertainty embedded in option premiums.

Implied Volatility Percentile

Implied volatility percentile is the percentage of observations in a selected historical window that had implied volatility below the current level.

Implied Volatility Rank

Implied volatility rank places current implied volatility within its high-to-low range over a selected lookback period, usually on a scale from 0 to 100.

L

2 terms

Lambda (Omega)

Lambda, also called omega, is the option Greek that measures the percentage change in an option’s value for a 1% move in the underlying price.

Local Volatility

Local volatility is the instantaneous volatility a pricing model assigns to each underlying price level and date, calibrated from option prices with the Dupire formula.

M

1 term

Market Volatility

Market volatility is the dispersion of an asset’s or index’s returns, usually quoted as an annualized standard deviation, and it measures move size, not direction.

O

1 term

Option Greeks

Option Greeks are risk measures, including delta, gamma, theta, vega, and rho, that estimate how an option’s value responds to price, time, volatility, and rates.

R

2 terms

Realized Volatility

Realized volatility is the annualized standard deviation of an underlying asset’s observed returns over a defined historical period.

Rho

Rho is the option Greek that estimates how much an option’s theoretical value changes when interest rates rise one percentage point, with other inputs held constant.

S

2 terms

Speed (Option Greek)

Speed is the third-order option Greek that measures how fast gamma changes as the underlying price moves, the third derivative of option value with respect to spot.

Sticky Strike and Sticky Delta

Sticky strike and sticky delta are rules for how implied volatility responds to a spot move: sticky strike holds IV fixed at each strike, sticky delta at each delta.

T

3 terms

Tail Risk

Tail risk is exposure to extreme outcomes at the far ends of a return distribution, estimated with tail measures such as Value at Risk and expected shortfall.

Theta

Theta is the option Greek that measures the change in an option’s theoretical value as one day passes, with the other pricing inputs held constant.

Time Decay

Time decay is the reduction in an option’s theoretical value caused by the passage of time, as its extrinsic value converges to zero at expiration.

V

15 terms

Vanna

Vanna is the second-order option Greek that measures how delta changes when implied volatility changes, or equivalently how vega changes as the underlying price moves.

Variance Swap

A variance swap is a forward contract on realized variance that pays the difference between realized variance and a fixed variance strike, times a variance notional.

Vega

Vega is the option Greek that measures the change in an option’s theoretical value for a one-percentage-point change in implied volatility, other inputs held constant.

Veta

Veta is the second-order option Greek that measures how vega changes as time passes, with spot, implied volatility, rates and dividends held fixed.

VIX (CBOE Volatility Index)

The VIX is Cboe’s index of the market’s expected 30-day volatility of the S&P 500, implied from SPX option prices and quoted in annualized percentage points.

VIX Futures

VIX futures are cash-settled contracts on the VIX value at a future settlement date, with each standard VX contract gaining or losing $1,000 per index point.

Volatility Arbitrage

Volatility arbitrage is a delta-hedged options strategy that trades the gap between implied volatility and the volatility the underlying is forecast to realize.

Volatility Cone

A volatility cone is a chart of realized-volatility percentiles across lookback windows, used to judge whether implied volatility is high or low at each horizon.

Volatility Risk Premium

The volatility risk premium is compensation embedded in option prices, measured as implied volatility minus expected or realized volatility over the same horizon.

Volatility Skew

Volatility skew is the pattern of different implied volatilities across option strikes for the same underlying and expiration.

Volatility Smile

A volatility smile is a U-shaped pattern in which lower- and higher-strike options share one expiration but imply more volatility than near-the-money options.

Volatility Surface

A volatility surface is a map of an underlying’s implied volatility across both option strike or delta and time to expiration at one market snapshot.

Volatility Term Structure

Volatility term structure is the pattern of implied volatility across option expirations for comparable strikes or deltas on the same underlying.

Vomma

Vomma, also called volga, is the second-order option Greek that measures how vega changes with implied volatility, giving the curvature of volatility exposure.

VVIX

VVIX is Cboe’s 30-day volatility-of-volatility index derived from VIX option prices and expressed as an annualized percentage.

Z

1 term

Zomma

Zomma is the third-order option Greek that measures how gamma changes when implied volatility changes, showing whether a gamma profile flattens or sharpens.

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