Ken Arrow famously modeled markets for risk by studying state-contingent contracts. But modern financial derivatives don't look like this! Gold futures, oil options, etc are contracts on prices. In this paper, we analyze a model where agents trade price-contingent contracts
Price-contingent contracts are incomplete: they do not achieve all the risk-sharing possibilities of richer Arrow securities, leaving agents exposed to unspanned basis risk. But we show, in our model, price-linked contracts optimally share the component of risk spanned by prices
The study of price-linked contracts links nicely to Black-Scholes theory: it turns out price-risk markets are markets for Greeks. Agents have linear (delta) and quadratic (gamma) exposure to spot prices; futures trade the linear component, variance swaps the quadratic part
In the process, we ask: why do options market exist? Do they play any role in improving social risk sharing? While the study of options is decades old, this question is surprisingly difficult to answer. We provide a simple story for why options markets are welfare-improving
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