Implied Volatility Surface Basics

The implied volatility surface maps how implied volatility varies across strikes and expirations—a topography of market expectations. Reading this surface reveals sentiment about tail risks, event timing, and relative value across the options chain.

Data Inputs and Provenance

Data Sources

• Exchange quotes: Use mid-prices from exchange bid/ask for liquid contracts
• Trade prices: Last trade may be stale; prefer quoted markets
• Broker marks: End-of-day valuations may include stale or modeled values
• Vendor feeds: Bloomberg, Refinitiv provide consolidated surfaces

Data Quality Checks

• Verify bid/ask spread is reasonable (wide spreads indicate illiquidity)
• Exclude options with zero volume and wide markets
• Timestamp all data; surfaces become stale within hours during volatile periods
• Cross-check with recent trades when available

Key Definitions

Smile: The pattern where OTM puts and calls have higher implied volatility than ATM options, creating a U-shape when plotted by strike.

Skew: The asymmetry where OTM puts trade at higher IV than OTM calls (equity skew) or vice versa (commodity skew).

Term structure: How ATM implied volatility changes across expirations—typically upward-sloping in calm markets, inverted during stress.

Modeling and Interpolation Choices

When building a smooth surface from discrete market quotes, choices include:

SVI (Stochastic Volatility Inspired) parameterization: The SVI model fits total variance w(k) = a + b(ρ(k-m) + √((k-m)² + σ²))

Where k = log-moneyness, and parameters (a, b, ρ, m, σ) are calibrated to market quotes.

Advantages:

• Parsimonious (5 parameters per slice)
• Arbitrage-free construction possible
• Smooth interpolation between quoted strikes

Alternative approaches:

• Spline interpolation (flexible but may introduce arbitrage)
• Polynomial fits (simple but poor tail behavior)
• SABR model (for rates/FX markets)

Parameter ρ in SVI controls skew direction: ρ < 0 produces equity-style downside skew.

Sticky Delta vs. Sticky Strike

Two conventions for how the surface moves with spot:

Sticky Strike: When spot moves, the IV at a fixed strike K remains constant. The surface is anchored to absolute strikes.

Sticky Delta: When spot moves, the IV at a fixed delta (e.g., 25-delta put) remains constant. The surface moves with spot.

Reality often falls between these extremes. Monitor which regime applies in current market conditions.

Use Cases for Trading and Risk

Trade Identification

• Skew trades: If 25-delta put IV = 34% vs. ATM = 28% (6% skew), compare to historical average (5%). Rich skew suggests selling OTM puts.
• Calendar trades: If 1-month ATM IV = 25% and 6-month ATM IV = 22%, term structure is inverted. Consider selling near-term vol, buying deferred.
• Butterfly trades: Profit from realized volatility being close to ATM expectation.

Risk Management

• Scenario analysis: Shift surface up 5 vols, steepen skew 2 vols, observe portfolio P/L
• Greeks aggregation: Calculate position vega by strike bucket and expiration
• Limit monitoring: Set limits on vega exposure to different surface regions

Pricing Exotics

Barrier options, variance swaps, and other exotics depend on the full surface, not just ATM vol. An accurate surface is essential for:

• Barrier pricing (spot path crosses strikes)
• Variance swap fair value (integrates over all strikes)
• Cliquet payoffs (forward-starting options)

Sample Surface Data

Equity Index Surface (S&P 500 style):

Observations:

• Downside skew: 25Δ put (34%) trades 10 vols above ATM (24%) in 1-month
• Term structure: ATM IV declines from 24% (1M) to 22% (6M)—normal contango
• Call wing: Flat, reflecting less demand for upside protection

Surface Monitoring and Drift

Track surface changes over time to identify regime shifts:

Daily checks:

• ATM IV level vs. 20-day average
• Skew (25Δ put - 25Δ call) vs. historical
• Term structure slope (6M - 1M)

Alert triggers:

• ATM IV moves >3 vols from prior day
• Skew moves >2 vols from 20-day average
• Term structure inverts (near-term > long-term)

These shifts signal changing market sentiment and may require position adjustment or hedging review.

Next Steps

For interpreting what smiles and skews signal about market sentiment, see Smile and Skew Interpretation.

To understand how term structure affects calendar trades, review Volatility Term Structure Modeling.