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Volatility Surface: Comparing Implied Volatility by Strike and Expiry

For educational purposes only; not investment advice.

Direct answer

Section titled “Direct answer”

An implied-volatility surface maps option IV across two dimensions: strike or moneyness, and time to expiration. Each expiration contributes a smile or skew slice; comparing those slices adds the volatility term structure. The surface is a compact representation of option prices under stated model, forward, rate, dividend, and quotation conventions.

It is not a forecast showing where the stock will trade. Nor is every point a market observation: listed quotes are discrete, so many displayed nodes are interpolated or extrapolated model values. A useful surface must distinguish executable data from estimates and satisfy economically coherent price constraints.

The surface’s three layers

Section titled “The surface’s three layers”
  1. Strike dimension: For a fixed expiry, IV changes across strike, Delta, or log-forward moneyness k = ln(K/F_T). Curvature is called a smile; asymmetry is commonly called skew.
  2. Maturity dimension: ATM and wing IV differ across expirations. For cross-maturity work, total variance w(k,T) = IV² × T is often more informative than raw annualized IV.
  3. Dynamics: After spot, time, or an event changes, the entire surface can shift, steepen, flatten, twist, or develop local kinks. A static surface says nothing by itself about the rule governing its next move.

Construct the surface from synchronized two-sided quotes. Infer forwards and discounting consistently, convert strikes into one moneyness coordinate, invert prices to IV with one convention, filter bad nodes, and fit or interpolate between valid observations. Label every fitted node separately from an executable Bid/Ask.

Static no-arbitrage conditions belong in price space. Within an expiry, ordinary Call prices should decrease and remain convex with strike. Across expirations, a standard construction should avoid invalid calendar relationships when compared in consistent forward coordinates. Smooth-looking IV is insufficient: interpolation can create negative implied densities or calendar crossings after conversion back to prices.

Reading two surface slices

Section titled “Reading two surface slices”

Suppose synchronized quotes produce this simplified grid:

Expiry k = -0.10 k = 0.00 k = +0.10
30 days 34% 28% 27%
180 days 30% 25% 24%

The 30-day left-wing skew is 34% − 28% = 6 volatility points; the 180-day difference is 30% − 25% = 5 points. Short-dated ATM IV is also 28% − 25% = 3 points above long-dated ATM IV. This grid therefore contains both downside skew and a downward IV term structure.

Raw IV does not equal accumulated uncertainty. Using 365-day time and ATM values:

w_30 = 0.28² × (30/365) = 0.00644

w_180 = 0.25² × (180/365) = 0.03082

The longer option has lower annualized IV but much greater total variance because it spans more time. It would be wrong to call it “cheaper volatility” solely from 25% < 28%. Price, Vega, carry, events, and the desired horizon must also be compared.

Analysis and risk controls

Section titled “Analysis and risk controls”
  • Synchronize underlying, option, rate, dividend, and corporate-action inputs; do not combine closing IVs recorded at different times.
  • Reject stale, crossed, zero-bid, or abnormally wide quotes and document liquidity thresholds.
  • Use consistent forward moneyness, day count, exercise style, settlement, and IV model across nodes.
  • Mark quoted, interpolated, and extrapolated nodes distinctly; uncertainty grows quickly in sparse wings and maturities.
  • Check strike monotonicity, convexity, nonnegative total variance, and cross-expiry calendar conditions in price space.
  • Preserve explainable event kinks rather than smoothing earnings or macro risk away.
  • Compare the same coordinate through time; fixed strikes change moneyness when spot moves.
  • Stress IV level, skew, curvature, term structure, spot, time, spread widening, and surface dynamics jointly.
  • Revalue each leg under full scenarios; aggregate Vega can hide expiry- and strike-bucket exposure.
  • Confirm early exercise, assignment, expiration, settlement, adjusted deliverables, and broker margin rules.
  • Version data, forward assumptions, filters, fitter, constraints, and fallbacks so marks are reproducible.

Common misconceptions

Section titled “Common misconceptions”
  • “The surface predicts the future stock-price distribution.” It is model-implied risk-neutral pricing information, not a physical forecast.
  • “Every displayed point is tradable.” Most grids contain interpolated mids or extrapolated wings.
  • “Highest IV means the best option to sell.” High IV can compensate for tail, event, liquidity, and gap risk.
  • “Lower long-dated IV means less uncertainty.” Annualized IV and total variance answer different questions.
  • “One ATM term structure describes the surface.” It omits skew, curvature, and their maturity dependence.
  • “A smooth surface is arbitrage-free.” Smoothness does not guarantee valid option-price monotonicity, convexity, or calendars.
  • “The surface stays fixed when spot moves.” Sticky-strike, sticky-Delta, and model dynamics produce different P&L.
  • “Net Vega zero removes surface risk.” Bucket exposures can offset locally and then diverge under a twist.
Section titled “Related topics”

Authoritative sources

Section titled “Authoritative sources”