Modeling the Private-to-Public Transition: IPOs, Direct Listings and De-SPAC Mergers

We have developed a comprehensive mathematical framework that delineates the complete transition of a firm from private to public ownership. This framework explicitly formalizes the endogenous decision to list, pre-listing restructuring, regulatory feasibility constraints, information production, pricing and allocation mechanisms, and post-listing market dynamics. A unified structure is employed to represent traditional IPOs, direct listings, and de-SPAC mergers. The proposed framework integrates the concepts of information asymmetry, free-float constraints, and market impact with equilibrium offer prices, first-day returns, and post-listing volatility. This integration enables the formulation of testable predictions across a range of listing mechanisms.