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AbstractIn this paper, we discuss the dynamic equilibrium of market making with price competition and incomplete information. The arrival of market sell/buy orders follows a pure jump process with intensity depending on bid/ask spreads among market makers and having a looping countermonotonic structure. We solve the problem with the nonzero-sum stochastic differential game approach and characterize the equilibrium value function with a coupled system of Hamilton–Jacobi nonlinear ordinary differential equations. We prove, do not assume a priori, that the generalized Issac's condition is satisfied, which ensures the existence and uniqueness of Nash equilibrium. We also perform some numerical tests that show our model produces tighter bid/ask spreads than those derived using a benchmark model without price competition, which indicates the market liquidity would be enhanced in the presence of price competition of market makers.

It is a well‐known anomaly that prices of put options are too high when options are out‐of‐the‐money. This paper presents a simple general equilibrium model of the market where European put options become substantially overpriced when they are out‐of‐the‐money. Overpricing is due to the presence of short‐sale constraints on trading stocks and derivatives, as well as the heterogeneity between investors. We confirm the predicting power of the model by comparing its implications with existing empirical results.