Volatility Surface Fundamentals and Geometry
Where analysis begins
Implied volatility is not a single number — it is a surface that extends across strikes and expiries, and its shape encodes information about market expectations, risk appetite, and positioning. This track introduces the foundational geometry of that surface: how it is constructed from observable option prices, what the axes represent, and how the surface evolves through time. The concepts of implied versus realised volatility are examined carefully, with attention to what the gap between them does and does not indicate. Surface interpolation methods are introduced alongside their assumptions, so that the analytical consumer understands the limitations of any surface representation they encounter. No prior options knowledge is assumed. The track builds from first principles, using plain language to establish intuition before introducing the mathematical notation that formal surface analysis requires. By the conclusion of this track, the analytical framework necessary to read a volatility surface with genuine comprehension is firmly in place — a foundation upon which every subsequent track depends.
- Implied versus realised volatility: a precise conceptual distinction
- Surface construction from observable option price data
- Interpolation methods and their embedded assumptions
- Reading surface shape as a carrier of market information