Structural Isomorphism Between Grid Trading and Option Writing: From Constrained Random Walk to Dynamic Volatility Management

Grid trading is nearly absent from the academic finance literature, dismissed as a simplistic retail strategy. This paper challenges that dismissal by establishing a formal structural isomorphism between grid trading and short put option writing: both belong to the short volatility strategy family, sharing identical risk structures and survival conditions. We prove three results. First, Payoff Isomorphism: the survival of both strategies reduces to a first-passage time condition τ_B > T on a bou