Gamma Capture 0-DTE Analytics for short-term traders. Developed in conjunction with Lehigh University.
Gamma Capture 0-DTE Analytics for short-term traders. Developed in conjunction with Lehigh University.
Call Premium = PV * Σ i∈{−range,+range} : MAX[ (S + b * x_net_i) − K, 0 ] × Prob_Skellam( x_net_i ; μ+, μ− )
Put Premium = PV * Σ i∈{−range,+range} : MAX[ K - (S + b * x_net_i), 0 ] × Prob_Skellam( x_net_i ; μ+, μ− )
Gamma Capture Crossing Intensity per Strike (K)
λ(K) = λ₀ + K_add_c + n * φ (K > ATM)
λ(K) = λ₀ + K_add_p + n/φ (K < ATM)
Gamma Capture is similar to asking how many bricks λ(K) and what cost per brick (b) does it take to build a brick wall? How many buy and sell limit orders (barrier widths) does the price need to cross to sum to an options premium? Gamma Capture is the mathematical expression for delta hedging an option. The formula measures the realized volatility that a vol trader earns by placing bids and offers (up/down barriers) into the market. Put-Call Parity and Monotonicity hold.
Geometric Brownian Motion
Var[ log price change ] = Var[ΔlogS] = σ² * time
Gamma Capture Motion
Var[ dollar price change ] = Var[ΔS] = barrier width² * Number of crossings
Geometric Brownian Motion accumulates variance continuously over time. Gamma Capture, however, earns variance by crossing discrete barriers. No crossings, no variance. Time decay happens because as time passes without a crossing, the variance window narrows. The probability of reaching Out-the-Money (OTM) strikes shrinks. In traditional 0-DTE options pricing models, gamma explodes and theta crashes as expiration approaches. The Gamma Capture model turns risk into reality by counting barrier crossings.
Reference:
"From Barrier Crossings to Terminal Distributions: A Skellam-Based Options Pricing Framework for 0-DTE Markets" (January 06, 2026).
Available on SSRN: https://ssrn.com/abstract=7029658
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