The Black-Scholes options model assumes that price paths are smooth and continuous. It is wrong at the wings, and corrects by having a different volatility at every strike. Gamma Capture prices options assuming the world jumps, and the wing premium falls out automatically — because in a world full of intraday price jumps, far-away options are genuinely more valuable than what a BS model says.
Black-Scholes
• Assumes continuous Gaussian diffusion
• Single σ cannot price wings correctly
• OTM options underpriced using only ATM vol
• iVol Smile added strike-by-strike as a patch
• Requires full iVol surface: σ(K,T)
• Different σ for each option — internally inconsistent
• Jump risk not modeled directly — jump premium hidden in smile
Gamma Capture
• Discrete jump process — fat tails by construction
• Wing prices emerge from jump term naturally
• No smile adjustment needed at flat Gamma Capture vol
• One parameter set prices entire surface
• Skew from p↑ ≠ p↓ (order-flow asymmetry)
• λ = σ²/b² ties vol directly to execution rate
• Internally consistent — no strike-by-strike override
Authors Euan Sinclair and Chris Merrill wrote about barrier crossings in their paper "Volatility Estimation via First Exit Times". Andersen, Dobrev & Schaumburg wrote "Duration-Based Volatility Estimation". And in his paper titled "Mathematical Analysis of Random Noise" by S.O. Rice, he derived a formula counting the average number of times a random process crosses a fixed level per unit time. Gamma Capture uses the same mathematical concepts, but applies them to intraday market prices. Gamma Capture is the first commercially available, in production volatility measure of its kind.