Special Purpose Vehicle (SPV) Pricing Using Physics-Informed Neural Networks

Many private stocks trade via SPV wrappers with hedge fund–style fees, creating systematic discounts. Because liquidations are random, fixed-maturity option pricing models misspecify timing risk. In this presentation, the pricing problem is formulated in a stochastic-expiry extension of the Black–Scholes model that incorporates management and carry, which yields a modified differential equation. A physics-informed neural network (PINN) solves this equation by enforcing the differential operator and boundary conditions. After training on simulated scenarios, the model generalizes to real trades and delivers consistent, data-efficient discount estimates for SPV-wrapped positions.