Equilibrium Liquidity Premia under Hedging Pressure and Margin Constraints
We develop a continuous-time equilibrium model of futures markets in which heterogeneous hedgers and speculators trade under explicit margin constraints. Agents maximize exponential utility and take prices as given, while the equilibrium futures drift is determined endogenously through market clearing. Margin frictions interact with risk-sharing motives to generate a nonlinear fixed-point problem linking individual optimality to aggregate consistency. The equilibrium is characterized by a coupled Hamilton. Jacobi-Bellman (HJB) and backward stochastic differential equation (BSDE) system, and we establish existence and uniqueness of the equilibrium drift under mild regularity conditions. A central contribution of the framework is a new geometric characterization of margin effects: margin constraints create no-trade regions in drift space, producing a frictional wedge that forces the equilibrium drift to be the projection of the frictionless Keynes-Hicks drift onto a margin-dependent interval. This yields a kinked and convex mapping from margin tightness to liquidity premia, with one-for-one amplification when the frictionless drift lies outside the wedge and flat sensitivity once it lies inside. Unlike Brunnermeier-Pedersen [2009] and Gârleanu-Pedersen [2011], whose margin effects are linear and exogenous, our model delivers a fully dynamic, state-dependent amplification mechanism arising endogenously from equilibrium price formation. The structure provides a tractable foundation for empirical implementation using disaggregated trader positions. Using CFTC gold-futures data and CME volatility measures, we find strong empirical support for the model’s nonlinear amplification mechanism: hedging pressure alone has no predictive power; margin tightness exerts a negative baseline effect; the interaction between hedging pressure and margin tightness generates a statistically significant kink; and volatility sharply magnifies the impact of margin tightness, producing the largest and most significant effect in the data. These findings confirm the model’s core prediction that margin constraints generate nonlinear, state-dependent, and volatility-amplified liquidity premia, providing the first structural empirical evidence for a kinked margin-pressure mechanism derived from a full HJB-BSDE equilibrium.