The volatility surface is a three-dimensional representation of implied volatility across all strikes and expirations for a given underlying. Rather than a single 'implied volatility' number, institutions think in terms of this entire surface — how IV varies by moneyness (the volatility skew) and by time to expiration (the term structure). The skew exists because demand for downside protection (puts) typically exceeds demand for upside speculation (calls), causing OTM puts to be priced at higher implied volatilities than ATM options. This is the 'volatility smile' or 'smirk.'

The term structure of volatility shows how implied volatility changes across different expirations. In normal markets, the term structure is upward-sloping (longer-dated options have higher IV because more time = more uncertainty). Before major events (earnings, FOMC, elections), the term structure can develop 'humps' where the event-specific expiration has elevated IV relative to surrounding expirations. After the event, the IV on that expiration collapses (IV crush), and the term structure normalizes. Institutional vol traders actively trade these term structure dislocations.

Surface dynamics drive sophisticated strategies. Skew trades involve buying and selling options at different strikes to express a view on how the skew will change. Calendar spreads trade the term structure by going long one expiration and short another. Vanna (the sensitivity of delta to IV changes) and volga (the sensitivity of vega to IV changes) are second-order Greeks that become critical when managing large options books. Market makers must hedge these higher-order risks continuously, which creates observable patterns in how the surface moves intraday.

Modern volatility surface modeling extends beyond Black-Scholes to stochastic volatility models (Heston, SABR) that capture the dynamics of how the surface moves over time. The SABR model is standard in rates markets. Local volatility models (Dupire) provide a different approach by deriving a deterministic volatility function from observed market prices. Each model has strengths and weaknesses — no single model perfectly captures all surface dynamics. Quant desks at major dealers calibrate multiple models daily and use them to identify relative value opportunities across the surface.