Model uncertainty and liquidity

Abstract

Extreme market outcomes are often followed by a lack of liquidity and a lack of trade. This market collapse seems particularly acute for markets where traders rely heavily on a specific empirical model such as in derivative markets like the market for mortgage backed securities or credit derivatives. Moreover, the observed behavior of traders and institutions that places a large emphasis on “worst-case scenarios” through the use of “stress testing” and “Value-at-Risk” seems different than Savage expected utility would suggest. In this paper, we capture model-uncertainty using an Epstein and Wang [Epstein, L.G., Wang, T., 1994. Intertemporal asset pricing under Knightian uncertainty. Econometrica 62, 283–322] uncertainty-averse utility function with an ambiguous underlying asset-returns distribution. To explore the connection of uncertainty with liquidity, we specify a simple market where a monopolist financial intermediary makes a market for a propriety derivative security. The market-maker chooses bid and ask prices for the derivative, then, conditional on trade in this market, chooses an optimal portfolio and consumption. We explore how uncertainty can increase the bid–ask spread and, hence, reduces liquidity. Our infinite-horizon example produces short, dramatic decreases in liquidity even though the underlying environment is stationary. We show how these liquidity crises are closely linked to the uncertainty aversion effect on the optimal portfolio. Effectively, the uncertainty aversion can, at times, limit the ability of the market-maker to hedge a position and thus reduces the desirability of trade, and hence, liquidity.