Markets for Price Risk

Feb 1, 2026

Baiyang Han, Junyi Hu, Anthony Lee Zhang

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Many financial contracts -- futures, options, and swaps -- are written on endogenous prices rather than primitive states of the world. How well can such markets approximate Arrow (1964)'s state-contingent contracts? We develop a tractable equilibrium model in which spot markets allocate goods efficiently but create wealth exposures to equilibrium prices. In our model, futures and variance swaps achieve price-contingent completeness: a planner restricted to price-contingent wealth transfers cannot Pareto-improve on equilibrium. Low-dimensional price derivatives therefore implement optimal risk sharing over the component of wealth risk spanned by prices, while leaving residual basis risk uninsurable. Our framework unifies classic results on futures markets and identifies a new role for variance markets in socially beneficial risk sharing.


Baiyang Han

Baiyang Han

Junyi Hu

Junyi Hu

Anthony Lee Zhang

Anthony Lee Zhang

University of Chicago Booth School of Business