What Is Implied Volatility?

What Is Implied Volatility?

Open any pricing model and feed it the observed market price of a specific option. The model has six standard inputs: spot, strike, time to expiry, risk-free rate, dividend yield, and volatility. The first five are observable. The sixth, volatility, is not. Implied volatility is the value of that sixth input that makes the model output equal to the market price.

Crucially, IV is not a property of the underlying. It is a property of the option contract under a chosen model. Different models produce different implied volatilities for the same option, because different models use different stochastic structures to map volatility into price. The Black-Scholes IV of an SPY 30-delta put is not the Heston IV of the same put. They calibrate to the same dollar price but they describe different things.

The number that retail traders see on broker screens (the "IV" column on every options chain) is almost always Black-Scholes implied volatility. It is the BSM volatility input that reproduces the mid-market quote. This is operationally useful but conceptually shaky: BSM assumes constant volatility and log-normal returns, neither of which holds in real markets, so BSM-implied volatility varies systematically across strike and tenor (skew + term structure) precisely because the model's assumption is wrong.

Why It Exists

The market does not quote options in volatility. It quotes options in dollar prices. IV is a derived quantity: traders invert the pricing model to extract the volatility that the market is "implying" through its dollar quote. Three reasons IV is the dominant analytic representation:

• Comparability across strikes and tenors. A 0.50 dollar premium on a 7-day SPY call is incomparable to a 5.00 dollar premium on a 90-day SPY call. But 14% IV on the 7-day vs 18% IV on the 90-day is directly comparable. IV normalizes premium across expiration and moneyness.
• Comparability across underlyings. A 1.00 dollar premium on a 50-dollar stock means something different than a 1.00 dollar premium on a 500-dollar stock. IV normalizes for underlying price level so volatilities can be compared across SPY, AAPL, TSLA, BTC, and 2000+ other names directly.
• Forward-looking expectation. IV reflects the market's expectation of future realized volatility plus a variance risk premium. Historical (realized) volatility is a backward-looking statistic. IV is forward-looking: it tells you what volatility option market makers think will obtain over the option's life.

How Each Pricing Model Computes IV

Each model defines IV through its own calibration to market quotes. Knowing which model you're working in matters because the same option will produce different IVs under each:

• Black-Scholes: single scalar volatility input. BSM IV is the most common and is what every retail platform reports. Because BSM assumes flat constant vol, the BSM-implied IV varies across strikes (skew) and tenors (term structure), which is the empirical signature that the model's assumption is wrong.
• Heston: there is no single Heston IV per option. Heston is a stochastic-vol model with five parameters (kappa, theta, nu, rho, v_0). Calibration finds parameter values that make Heston match the entire surface jointly. The "Heston-implied" volatility surface is implicit in the parameter set, not a single number per option.
• SABR: calibrated per expiration with parameters (alpha, beta, rho, nu). The Hagan formula gives a closed-form approximation of the SABR-implied smile. SABR-implied IV at any strike is what the calibrated SABR model says that strike's BS-equivalent vol would be.
• Local volatility: Dupire's local-vol function sigma(S, t) is the surface that perfectly matches every option price. It is a function of spot and time, not of strike. The "local IV" for a specific option is the average of sigma(S, t) over the relevant region of (S, t) space.
• Jump diffusion: calibrated through (sigma, lambda, mu_J, sigma_J). The jump-aware IV surface fits short-tenor smile better than continuous-vol models, capturing the jump-risk premium that diffusion-only models miss.

Worked Example

SPY at 510, 30-day expiration, 510 strike call quoting at 7.20 dollars. Risk-free rate 4.5%, dividend yield 1.3%. Inverting Black-Scholes:

• BSM IV = 14.4%

Now invert Heston with kappa=2.0, theta=0.025, nu=0.45, rho=-0.7, v_0=0.024 calibrated to the rest of the SPY surface. Heston produces a price of 7.20 too (the surface was calibrated to match). The "Heston IV" at 510 strike from the calibrated parameter set, expressed in BS-equivalent units, is 14.5%. They agree closely at-the-money. They disagree by 60-150 basis points at 25-delta put or 25-delta call, because the models have different surface shapes.

This is not a problem - it is the point. The disagreement is the model-divergence signal: it tells you which model thinks the option is rich and which thinks it is cheap.

IV Rank, IV Percentile, and Why They Matter

IV by itself is hard to interpret. 18% IV on AAPL is below average; 18% IV on KO is well above average. Two normalizing metrics fix this:

• IV Rank: where current IV sits in its trailing 52-week range (0% = at the 52-week low, 100% = at the 52-week high). IV Rank above 50% indicates elevated vol relative to recent history; above 80% is typically extreme.
• IV Percentile: what percentage of trading days over the trailing 52-weeks closed at lower IV than today. More robust than IV Rank because it accounts for distribution shape, not just min/max.

Both are operationally useful for sizing premium-collection vs premium-buying strategies. High IV Rank favors selling premium (statistical mean reversion). Low IV Rank favors buying premium (vol expansion potential). Neither is a complete signal: a name in a regime-shift trades at sustained high IV that does not mean-revert.

Common Misreadings

• "IV is high so options are overpriced." Possibly true, but IV is high for a reason. Earnings, FDA decisions, M&A, and macro events all raise IV legitimately. Selling elevated IV before known event prints is selling event premium, not capturing mean reversion.
• "IV is the probability the option finishes ITM." No. IV is the volatility parameter. The probability of ITM expiration is computable from IV plus the rest of the model state, but IV itself is not a probability.
• "IV is what realized volatility will be." No. IV is a forward-looking expectation under the risk-neutral measure, which differs from the real-world expectation by the variance risk premium. On average, IV exceeds subsequent realized vol by 2-4 vol points, which is the premium that funds the historical edge of short-vol strategies.

Related Concepts

Volatility Skew · Volatility Smile · Term Structure · IV Crush · Variance Risk Premium · IV vs HV History · Pricing Model Landscape

References & Further Reading

• Black, F. and Scholes, M. (1973). "The Pricing of Options and Corporate Liabilities." Journal of Political Economy, 81(3), 637-654. The original definition of IV by inversion.
• Gatheral, J. (2006). The Volatility Surface: A Practitioner's Guide. Wiley. Practitioner reference on how IV varies across strike and tenor.
• Bollerslev, T., Tauchen, G., and Zhou, H. (2009). "Expected Stock Returns and Variance Risk Premia." Review of Financial Studies, 22(11), 4463-4492. The IV vs RV decomposition.

View live SPY implied volatility surface and term structure ->

This page is part of the Pricing Model Landscape and the canonical reference set on options market structure. Browse all documentation.