The formation of share market prices under heterogeneous beliefs and common knowledge

Financial economic models often assume that investors know (or agree on) the fundamental value of the shares of the firm, easing the passage from the individual to the collective dimension of the financial system generated by the Share Exchange over time. Our model relaxes that heroic assumption of one unique "true value" and deals with the formation of share market prices through the dynamic formation of individual and social opinions (or beliefs) based upon a fundamental signal of economic performance and position of the firm, the forecast revision by heterogeneous individual investors, and their social mood or sentiment about the ongoing state of the market pricing process. Market clearing price formation is then featured by individual and group dynamics that make its collective dimension irreducible to its individual level. This dynamic holistic approach can be applied to better understand the market exuberance generated by the Share Exchange over time.Comment: 22 pages, 9 figure

Endogenous Correlation

We model endogenous correlation in asset returns via the role of heterogeneous expectations in investor types, and the dynamic impact of imitative learning by investors. Learning is driven by relative performance. In addition, we allow a cautious slow learning pace to reflect institutional conditions. Imitative learning shapes the market ecology that influences price formation. Using the model of non-imitative agents as a benchmark, our results show that the dynamics of imitative learning endogenously induce a significant degree of asset dependency and patterns of non-constant correlation. The asymmetric learning effect on correlation, however, implies a self-reinforcing process, where a bearish condition amplifies the effect that further exacerbates asset dependency. We conclude that imitative learning, even when rational, can to a certain extent account for the phenomena of market crashes. Our results have implications for transparency in regulation issues

Finance Applications of Game Theory

Traditional finance theory based on the assumptions of symmetric information and perfect and competitive markets has provided many important insights. These include the Modigliani and Miller Theorems, the CAPM, the Efficient Markets Hypothesis and continuous time finance. However, many empirical phenomena are difficult to reconcile with this traditional framework. Game theoretic techniques have allowed insights into a number of these. Many puzzles remain. This paper argues that recent advances in game theory concerned with higher order beliefs, informational cascades and heterogeneous prior beliefs have the potential to provide insights into some of these remaining puzzles.

Finance Applications of Game Theory

Traditional finance theory based on the assumptions of symmetric information and perfect and competitive markets has provided many important insights. These include the Modigliani and Miller Theorems, the CAPM, the Efficient Markets Hypothesis and continuous time finance. However, many empirical phenomena are difficult to reconcile with this traditional framework. Game theoretic techniques have allowed insights into a number of these. Many puzzles remain. This paper argues that recent advances in game theory concerned with higher order beliefs, informational cascades and heterogeneous prior beliefs have the potential to provide insights into some of these remaining puzzles.

Aggregation of Information and Beliefs: Asset Pricing Lessons from Prediction Markets

In a binary prediction market in which risk-neutral traders have heterogeneous prior beliefs and are allowed to invest a limited amount of money, the static rational expectations equilibrium price is demonstrated to underreact to information. This effect is consistent with a favorite-longshot bias, and is more pronounced when prior beliefs are more heterogeneous. Relaxing the assumptions of risk neutrality and bounded budget, underreaction to information also holds in a more general asset market with heterogeneous priors, provided traders have decreasing absolute risk aversion. In a dynamic asset market, the underreaction of the first period price is followed by momentum.prediction markets; private information; heterogeneous prior beliefs; limited budget; underreaction

Heterogeneity, Market Mechanisms, and Asset Price Dynamics

This chapter surveys the boundedly rational heterogeneous agent (BRHA) models of financial markets, to the development of which the authors and several co-authors have contributed in various papers. We give particular emphasis to role of the market clearing mechanism used, the utility function of the investors, the interaction of price and wealth dynamics, portfolio implications, the impact of stochastic elements on the markets dynamics, and calibration of this class of models. Due to agents’ behavioural features and market noise, the BRHA models are both nonlinear and stochastic. We show that the BRHA models produce both a locally stable fundamental equilibrium corresponding to that of standard paradigm, as well as instability with a consequent rich range of possible complex behaviours characterised both indirectly by simulation and directly by stochastic bifurcations. A calibrated model is able to reproduce quite well the stylized facts of financial markets. The BRHA framework is thus able to accommodate market features that seem not easily reconcilable for the standard financial market paradigm, such as fat tail, volatility clustering, large excursions from the fundamental and bubbles.Bounded rationality; interacting heterogeneous agents; behavioural finance; nonlinear economic dynamics; complexity

Why the Law Hates Speculators: Regulation and Private Ordering in the Market for OTC Derivatives

A wide variety of statutory and common law doctrines in American law evidence hostility towards speculation. Conventional economic theory, however, generally views speculation as an efficient form of trading that shifts risk to those who can bear it most easily and improves the accuracy of market prices. This Article reconciles the apparent conflict between legal tradition and economic theory by explaining why some forms of speculative trading may be inefficient. It presents a heterogeneous expectations model of speculative trading that offers important insights into antispeculation laws in general, and the ongoing debate concerning over-the-counter (OTC) derivatives in particular. Although trading in OTC derivatives is presently largely unregulated, the Commodity Futures Trading Commission recently announced its intention to consider substantively regulating OTC derivatives under the Commodity Exchange Act (CEA). Because the CEA is at heart an antispeculation law, the heterogeneous expectations model of speculation offers policy support for the CFTC\u27s claim of regulatory jurisdiction. This model also, however, suggests an alternative to the apparently binary choice now available to lawmakers (i. e., either regulate OTC derivatives under the CEA, or exempt them). That alternative would be to regulate OTC derivatives in the same manner that the common law traditionally regulated speculative contracts: as permitted, but legally unenforceable, agreements. By requiring derivatives traders to rely on private ordering to ensure the performance of their agreements, this strategy may offer significant advantages in discouraging welfare-reducing speculation based on heterogeneous expectations while protecting more beneficial forms of derivatives trading

Learning from experience in the stock market

We study the dynamics of a Lucas-tree model with finitely lived agents who "learn from experience." Individuals update expectations by Bayesian learning based on observations from their own lifetimes. In this model, the stock price exhibits stochastic boom-and-bust fluctuations around the rational expectations equilibrium. This heterogeneous-agents economy can be approximated by a representative-agent model with constant-gain learning, where the gain parameter is related to the survival rate. JEL Classification: G12, D83, D84assett pricing, bubbles, Heterogeneous Agents, Learning from experience, OLG

Optimal monetary policy with imperfect common knowledge

We study optimal nominal demand policy in an economy with monopolistic competition and flexible prices when firms have imperfect common knowledge about the shocks hitting the economy. Parametrizing firms´ information imperfections by a (Shannon) capacity parameter that constrains the amount of information flowing to each firm, we study how policy that minimizes a quadratic objective in output and prices depends on this parameter. When price setting decisions of firms are strategic complements, for a large range of capacity values optimal policy nominally accommodates mark-up shocks in the short-run. This finding is robust to the policy maker observing shocks imperfectly or being uncertain about firms´ capacity parameter. With persistent mark-up shocks accommodation may increase in the medium term, but decreases in the long-run thereby generating a hump-shaped price response and a slow reduction in output. Instead, when prices are strategic substitutes, policy tends to react restrictively to mark-up shocks. However, rational expectations equilibria may then not exist with small amounts of imperfect common knowledge