No-arbitrage, state prices and trade in thin financial markets

Abstract

We examine how non-competitiveness in financial markets affects the choice of asset portfolios and the determination of equilibrium prices. We apply a model of economic equilibrium, based on [12], in which individual traders recognize and estimate the impact of their trades on financial prices, and in which these effects are determined endogenously as part of the equilibrium concept. For the case in which markets allow for perfect insurance, we argue that the principle of no-arbitrage asset pricing is consistent with non-competitive behavior and extend the fundamental theorem of asset pricing to the non-competitive setting.

The Effect of Market Power on Risk-Sharing

“…of two agents. This comes in sharp contrast to models of Carvajal and Weretka [15], Kyle [37] and Weretka [53], where the two-agent game is in fact ill-posed. This should be highlighted, since many of the real-world risk-sharing transactions are between only two agents.…”

“…Recently, a number of equilibrium models have been established assuming that market's imperfection stems from market's thinness. More precisely, in Carvajal and Weretka [15] (see also Malamud and Rostek [41], Weretka [53] or Carvajal [13] for a broader discussion), a non-competitive market without asymmetric information is considered and (as in our paper) each agent submits demand functions taking into account the impact of her order in the equilibrium. The main substantial difference to our demand-function game is the imposed set of strategic choices.…”

“…The sum of these random endowments is called the aggregate endowment and is denoted by E := n i=1 E i . The preferences of agent i are modelled by the M-V utility 15 (2.1)…”

“…The main substantial difference to our demand-function game is the imposed set of strategic choices. According to the demand games in Carvajal and Weretka [15], Kyle [37] and Weretka [53] (see also Rostek and Weretka [48] for a dynamic version), each agent estimates the price impact of her order, (defined as the slope of the aggregate demand of the rest of the agents) and responds accordingly. Under linear demand functions however, the slope of the demands does not depend on agents' endowments and hence this demand game is not driven by the agents' motive to reveal hedging needs different from their true ones.…”

“…10 As already mentioned, the presence of noise traders and its impact on the equilibrium are addressed in Section 5 as an extension of our basic model. 11 Note also that although in Carvajal and Weretka [15] and Weretka [53] the agents' preferences are more general, the tractability of their models is based on the assumption of finite probability space.…”