Building the Surface

Markets hand you quotes, not functions: out-of-the-money puts and calls at listed strikes, over-the-counter quotes parameterized by delta, and index fear gauges in the VIX style. Building a tradable surface means interpolating and extrapolating these points into a continuous map of strike and expiry that contains no static arbitrage — no negative butterfly spreads and no calendar spreads that lose money for free. In practice desks fit a parametric shape such as SVI or SABR to each expiry, then interpolate the parameters through time. The discipline matters because every downstream pricer, hedge ratio, and risk report consumes this surface, and an arbitrage embedded in it silently corrupts them all.