Implied volatility surface explorer
Build an implied-volatility surface across strike and maturity, rotate it in 3D and see how skew, curvature and term structure each change its shape.
02 / IMPLIED VOLATILITY
Volatility surface
A new dimension to the shape of uncertainty.
Short-dated wings are more pronounced. Term slope changes how ATM volatility evolves with maturity; skew and curvature shape the smile across strikes.
About this surface +
An illustrative surface, not market data or an arbitrage-free calibration. σ(K,T) = σ₁Y × exp[term × (T − 1) + (skew × m + curvature × m²) / √(T + 0.25)], where m = K/F − 1 and T is in years. The forward F is held constant across expiries. Height and colour both encode annualised volatility; the vertical scale adjusts to the displayed range.
How to use it
Use the sliders to set the at-the-money level, skew, curvature and term slope. Drag the surface or use the arrow keys to rotate it, and inspect any point to read its strike, maturity and implied volatility.
What it teaches
A single Black–Scholes volatility cannot match option prices across strikes. Markets quote a surface instead. Skew tilts the smile so low strikes carry higher volatility, curvature lifts both wings, and term slope controls how at-the-money volatility changes with maturity.
Short-dated wings are more pronounced, which is one reason practitioners model the surface with stochastic volatility or jumps rather than one constant number. The surface here is a parametric teaching model, not live market data.
Learn the ideas behind it
- Reading the implied vol surface
- The empirical smile: fat tails, skew and the limits of Black–Scholes
- Why jumps are needed