This article reviews the theory of imperfectly competitive financial markets, with special attention to recent contributions and rapidly growing areas of research. We highlight the methodological advances that have led to a unified analytic framework for static, dynamic, centralized, and decentralized markets. Accounting for imperfect competition has not only reshaped our understanding of financial market data but also underscored the importance of market structure, motivated novel policy tools and objectives, and opened new avenues for market design. We identify areas where new models and techniques could enable further progress on equilibrium and market design analyses for markets with large players.

Most assets clear independently rather than jointly. This paper presents a model based on the uniform‐price double auction which accommodates arbitrary restrictions on market clearing, including independent clearing across assets (allowed when demand for each asset is contingent only on the price of that asset) and joint market clearing for all assets (required when demand for each asset is contingent on the prices of all assets). Additional trading protocols for traded assets—neutral when the market clears jointly—are generally not redundant innovations, even if all traders participate in all protocols. Multiple trading protocols that clear independently can be designed to be at least as efficient as joint market clearing for all assets. The change in price impact brought by independence in market clearing can overcome the loss of information, and enhance diversification and risk sharing. Except when the market is competitive, market characteristics should guide innovation in trading technology.

Decentralized trading motivates financial innovation, making synthetic products like derivatives nonredundant, even when all traders trade all assets. This nonredundancy arises because derivatives affect cross-security inference (information) and, in markets with large traders, equilibrium price impact (liquidity). The efficient securities differ from the underlying assets. While the market index/mutual funds are efficient in decentralized markets with competitive investors, heterogeneous portfolios that balance index tracking with liquidity transformation become efficient in markets with large traders. Efficient securities facilitate the trading of all fundamental risks but generally forgo hedging all contingencies to minimize the price impact costs associated with risk sharing and diversification.

We derive analytic valuation formulas for range accrual notes and spread range accrual notes under an affine term structure model with jump risks. We show that the value of a range accrual note can be significantly affected by the choice of interest rate model and the arrival intensity of jump risks. We also show that misuse of the correlation between reference rates of a spread range accrual note may lead traders and risk managers to mispricing of the note.