Gamma Capture Call Option
The premium is the sum of payouts, weight by the probability of each outcome. The up/down barrier (b) moves the stock price (S) by a fixed width.
Call Premium = PV × Σ i∈{−30,+30} : MAX[ (S + b * x_net_i) − K, 0 ] × Prob_Skellam( x_net_i ; μ+, μ− )
Up, Down ~ Poisson(λ * T/2) independently
Central Limit Theorem: For large μ and/or T, Prob_Skellam looks Gaussian and yields nearly identical results as the BSM.
Gamma Capture Crossing Intensity per Strike (K)
λ(K) = λ_ATM + |K−ATM| * K_mult * {φ calls; 1/φ puts}
Where the "Skew" Comes From
Gamma Capture derives this market asymmetry structurally. It calculates a simple count balance ratio:
φ = UP Crossings Count / DOWN Crossings Count