Analyzing Volatility Surfaces

Analyzing Volatility Surfaces

When To Use

• Constructing an implied volatility surface from option chain data across strikes and expirations
• Analyzing skew dynamics (put skew, call skew, smile shape) for a single underlier or cross-asset comparison
• Evaluating term structure of volatility for calendar spread positioning or structured product pricing
• Identifying vol surface anomalies that signal mispricing, liquidity dislocations, or event risk
• Supporting pricing or risk review of exotic/structured products that depend on vol surface interpolation

Inputs To Gather

• Option chain data: Bid/ask implied vols (or prices to back-solve) across strikes and expirations; specify underlier (equity index, single stock, FX pair, commodity)
• Underlier spot/forward: Current spot price, dividend yield or carry assumptions, and forward curve if available
• Expiration set: Which tenors to include (e.g., weekly, monthly, quarterly, LEAPS); confirm whether to use listed expirations or interpolated constant-maturity tenors
• Strike convention: Absolute strike, moneyness (K/S), delta-space, or log-moneyness — confirm which convention to use for surface construction
• Model context: Whether surface is for mark-to-market, exotic pricing (local vol, stochastic vol), or relative value analysis
• Reference date and market hours: As-of date/time for the snapshot; whether to use settlement vols or intraday marks

Workflow

1. Validate and clean input data

   • Filter out stale quotes, zero-volume strikes, and obvious bad ticks (e.g., implied vol < 1% or > 300%)
   • Flag wide bid/ask spreads — use mid-market only when spread is within acceptable threshold [VERIFY: firm-specific threshold]
   • Confirm put-call parity consistency; reconcile any violations by adjusting forward/dividend assumptions

2. Construct the raw surface

   • Map implied vols onto a strike × expiration grid using the chosen strike convention
   • For each expiration slice, fit a parametric curve (SVI, SABR, or cubic spline) or use raw market points
   • Interpolate across tenors to fill gaps — use variance-linear interpolation (total variance = σ²·T should increase monotonically in T)
   • Check for calendar spread arbitrage: total variance must be non-decreasing in maturity at every strike
   • Check for butterfly arbitrage: the local variance surface must produce non-negative probability densities

3. Analyze skew

   • Compute 25-delta risk reversal (25d call vol − 25d put vol) and 25-delta butterfly (average of 25d wings − ATM vol) for each tenor
   • Measure skew slope: dσ/dK or dσ/d(log-moneyness) around ATM
   • Compare current skew level to historical distribution (percentile rank over 1Y, 3Y windows)
   • Identify skew regime: steep/flat relative to realized skewness of returns, demand-driven vs. fundamental

4. Analyze term structure

   • Plot ATM vol across tenors; identify contango (upward-sloping) vs. backwardation (inverted)
   • Calculate vol carry: ATM implied vol minus short-dated realized vol at each tenor point
   • Flag event-driven kinks (earnings, FOMC, expiration clustering) that create localized term structure humps
   • Compare term structure shape to historical norms and cross-asset benchmarks

5. Assess surface dynamics and Greeks exposure

   • Estimate vega, vanna (dVega/dSpot), and volga (dVega/dVol) profiles across the surface
   • Identify regions of high convexity or sensitivity relevant to the portfolio or trade under review
   • If for exotic pricing: note where local vol or stochastic vol model choice materially affects valuation (e.g., barriers near skew-sensitive strikes)

6. Synthesize findings

   • Summarize surface shape, skew regime, and term structure posture
   • Highlight actionable observations: relative value opportunities, mispriced strikes, or risk concentrations
   • Flag any data quality issues or model-dependent conclusions

Output

• Surface summary table: ATM vols, 25d RR, 25d BF for each tenor
• Skew analysis section: Current skew metrics with historical percentile context; skew slope chart data
• Term structure section: ATM vol curve, vol carry estimates, event-adjusted term structure
• Arbitrage check results: Calendar and butterfly arbitrage flags with specific strike/tenor locations
• Key findings and trade implications: 3–5 bullet points with actionable takeaways
• Data quality notes: Stale quotes excluded, wide-spread strikes flagged, parity violations observed

Quality Checks

• Total variance is monotonically non-decreasing in maturity at every strike (no calendar arbitrage)
• Butterfly spreads produce non-negative payoffs at all points (no butterfly arbitrage)
• Interpolated surface reproduces input market quotes within bid/ask tolerance
• Strike convention and delta convention are applied consistently — do not mix sticky-strike and sticky-delta frameworks without explicit notation
• Skew and term structure metrics are compared to correct historical benchmarks (same underlier, same convention) [VERIFY: data source for historical vol percentiles]
• All implied vols are derived using the correct exercise style (American vs. European) and dividend treatment for the underlier [VERIFY: exercise convention for specific product]
• Mark any model-dependent conclusions (e.g., local vol extrapolation beyond liquid strikes) with explicit caveats