What is the volatility surface, and how do skew and term structure interact to shape it?

The volatility surface is a three-dimensional representation of implied volatility as a function of both strike price (or moneyness) and time to expiration. It captures the market's view of how uncertainty varies across different scenarios and horizons.\n\nThe Three Axes:\n\n`mermaid\ngraph TD\n A[\"Volatility Surface\"] --> B[\"X-Axis: Strike / Moneyness\"]\n A --> C[\"Y-Axis: Time to Expiry\"]\n A --> D[\"Z-Axis: Implied Volatility\"]\n B --> E[\"Skew / Smile
(cross-section at fixed T)\"]\n C --> F[\"Term Structure
(cross-section at fixed K)\"]\n E --> G[\"Combined = Full Surface\"]\n F --> G\n`\n\nVolatility Skew (Strike Dimension):\n\nFor equity indices, implied volatility typically decreases as strike increases (negative skew or \"smirk\"). This reflects:\n- Demand for downside protection (OTM puts are expensive)\n- Leverage effect (falling prices increase volatility)\n- Jump risk (crashes are more common than melt-ups)\n\nExample for Ashfield 500 Index at 4,200 with 60-day options:\n\n| Strike | Moneyness | Implied Vol |\n|---|---|---|\n| 3,780 | 90% | 24.5% |\n| 3,990 | 95% | 21.8% |\n| 4,200 | 100% (ATM) | 19.2% |\n| 4,410 | 105% | 17.9% |\n| 4,620 | 110% | 17.1% |\n\nTerm Structure (Time Dimension):\n\nImplied volatility also varies by expiration:\n- Normal (upward sloping): longer-dated options have higher IV, reflecting greater uncertainty\n- Inverted: near-term options have higher IV, common during crises or around events (earnings, elections)\n- Humped: IV peaks at an intermediate maturity (e.g., around an expected event date)\n\nWhy the Surface Matters:\n\n1. Exotic option pricing: Barrier options, Asian options, and other path-dependent instruments require the full surface, not a single flat volatility\n2. Risk management: Different parts of a portfolio may be sensitive to different regions of the surface\n3. Relative value: Traders identify cheap and expensive options by comparing market-implied surface to theoretical models\n4. Interpolation: For options at non-standard strikes or maturities, the surface provides a framework for consistent interpolation\n\nSurface Dynamics:\nThe surface is not static. It shifts, steepens, flattens, and twists over time. Key movements include:\n- Parallel shift: entire surface moves up or down (general vol change)\n- Skew steepening: OTM put vol rises faster than ATM vol (fear increasing)\n- Term structure inversion: near-term vol spikes above long-term vol (event risk)\n\nPractice volatility surface analysis in our CFA Derivatives question bank.