Stochastic equilibria of an asset pricing model with heterogeneous beliefs and random dividends (original) (raw)

Asset Market Dynamics in Equilibrium Models with Heterogeneous Agents: Analytical Results

Advances in Economics and Business, 2013

We examine market dynamics in a discretetime, Lucas-style asset-pricing model with heterogeneous, utility-optimizing agents. Finitely many agents trade a single asset paying a stochastic dividend. All agents know the probability distribution of the dividend but not the private information such as wealth and asset holdings of other agents. The market clearing price is determined endogenously in each period such that supply always equals demand. Our aim is to determine whether and how the pricing function evolves toward equilibrium. In the special case where all agents have logarithmic utility, but possibly different holdings and discount factors, we completely describe the market dynamics, including the evolution of the pricing and demand functions, and asset holdings of the agents. The market converges to a stable equilibrium state where only the most patient agents remain, and the equilibrium pricing function is the same as the one arising in the simple homogeneous setting.

A Dynamic Stochastic Model of Asset Pricing with Heterogeneous Beliefs

Computational Economics, 2010

This paper presents a new stochastic model of asset pricing, based on agents with heterogeneous beliefs. Forecasting rules of all agents are characterized by a stochastic term that works as an agent-based time dependent weight of the conditional expectation of the fundamental. Since we consider the presence of an imitative behavior between agents, these weights depend stochastically on the type-distribution of agents. The resulting dynamical system is firstly analyzed in a deterministic framework. Starting from the results obtained in the deterministic case, the model is lastly explored by reintroducing randomness. The deterministic study aims at providing the existence of a region in the parameters plane where the unique possible dynamics is the convergence to a steady state, while complexity is exhibited outside such region. This region is also analyzed by reintroducing stochasticity and we provide an explicit formula for its probability measure. Our findings are in agreement with the economic meaning of the parameters. Finally, we propose a bayesian analysis, in order to explore the distribution of the adjustment term of the proportion of agents.

Asset price dynamics with heterogeneous, boundedly rational, utility-optimizing agents⋆

We examine market dynamics in a discrete-time, Lucas-style asset-pricing model with heterogeneous, utility-optimizing agents. Finitely many agents trade a single asset paying a stochastic dividend, and know the probability distribution of the dividend but not the private information of other agents. The market clearing price is determined endogenously in each period such that supply always equals demand. The resulting market price and agents' demands are functions of the dividend; equilibrium means these functions are at steady-state. Our aim is to determine whether and how the pricing function evolves toward equilibrium. In case all agents have logarithmic utility, but possibly different hold-ings and discount factors, we completely describe the market dynamics, including the evolution of the pricing and demand functions, and asset holdings of the agents. The market converges to a stable equilibrium state where only the most patient agents remain, and the equilibrium pricing fu...

Endogenous fluctuations in a simple asset pricing model with heterogeneous agents

Journal of Economic Dynamics and Control, 2000

In this paper we study the adaptive rational equilibrium dynamics in a simple asset pricing model introduced by Brock and Hommes (System Dynamics in Economic and Financial Models, Wiley, Chichester, 1997, pp. 3}44; Journal of Economic Dynamics and Control, 22, 1998. Traders have heterogeneous expectations concerning future prices and update their beliefs according to a risk adjusted performance measure and to market conditions. Further, also their expectations about conditional variances of returns vary over time. We show that even for the simple case where agents can only choose between two di!erent predictors complicated dynamics arise and we analyse the bifurcation routes to chaos.

Asset Price Dynamics When Behavioural Heterogeneity Varies

Computational Economics, 2008

We build a model in which asset prices are expectationally driven and agents forecast future prices hinging on a combination of fundamental value, trend and inertia. The model has a unique steady state and we investigate its stability. In particular the amount of behavioural heterogeneity in the model is given by the number of intermediaries actually operating in the market: we are concerned with the effects that changing such number produces on the steady state in terms of stability. Assuming that the set of relevant intermediaries is sampled randomly we discuss the probability of having stability as a function of the market's parameters and the number of such agents. Our simulations show that stability in the multi-agent setting does not require that conditions for stability in the representative agent case be met for every individual; so stability can arise even if some of the agents would not be compatible with it if they were the only ones operating in the market. The same goes for instability. Further, we find that stabilising (or destabilising) effects of heterogeneity are not uniform across the market's essential characteristics, as captured by a given structural parameter: in fact we can identify a parametric region in which heterogeneity is stabilising and another in which it is destabilising.

Equilibria in financial markets with heterogeneous agents: a probabilistic perspective

Journal of Mathematical Economics, 2005

We analyse financial market models in which agents form their demand for an asset on the basis of their forecasts of future prices and where their forecasting rules may change over time, as a result of the influence of other traders. Agents will switch from one rule to another stochastically, and the price and profits process will reflect these switches. Among the possible rules are "chartist" or extrapolatory rules. Prices can exhibit transient behaviour when chartists predominate. However, if the probability that an agent will switch to being a "chartist" is not too high then the process does not explode. There are occasional bubbles but they inevitably burst. In fact, we prove that the limit distribution of the price process exists and is unique. This limit distribution may be thought of as the appropriate equilibrium notion for such markets. A number of characteristics of financial time series can be captured by this sort of model. In particular, the presence of chartists fattens the tails of the stationary distribution.

The dynamic behaviour of asset prices in disequilibrium: a survey

International Journal of Behavioural Accounting and Finance, 2011

This article surveys boundedly rational heterogeneous agent (BRHA) models of financial markets. We give particular emphasis to the role of the market clearing mechanism used, the utility function of the investors, the interaction of price and wealth dynamics, and calibration of this class of models. Due to agents' behavioural features and market noise, the BRHA class of models are both non-linear and stochastic. We show that BRHA models produce both a locally stable fundamental equilibrium corresponding to that of the standard paradigm, as well as instability with a consequent rich range of possible complex behaviours that are analysed by both simulation and deterministic bifurcation analysis. A calibrated model is able to reproduce quite well the stylised facts of financial markets. The BRHA framework seems able to better accommodate market features such as fat tails, volatility clustering, large excursions from the fundamental and bubbles than the standard financial market paradigm.

A dynamic stochastic asset pricing model with heterogeneous agents

2000

An interesting contribution is due to Brock and Hommes (1997) and (1998). The authors propose simple, analytically tractable heterogeneous agent mod- els to show that irrational strategies can survive evolutionary selection. They studied heterogeneity in expectation formation by introducing the concept of Adaptive Belief System (ABS) to model economic and flnancial models. In this paper heterogeneity is assumed, in fact

An analysis of the effect of noise in a heterogeneous agent financial market model

Journal of Economic Dynamics and Control, 2011

Heterogeneous agent models (HAMs) in finance and economics are often characterised by high dimensional nonlinear stochastic differential or difference systems. Because of the complexity of the interaction between the nonlinearities and noise, a commonly used indirect approach to the study of HAMs combines theoretical analysis of the underlying deterministic skeleton with numerical analysis of the stochastic model. However, a natural question to ask is whether this indirect approach properly characterises the nature of the stochastic model. This paper aims to tackle this question by developing a direct and analytical approach to the analysis of a stochastic model of speculative price dynamics involving two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the stationary measures of a stochastic dynamical system. Using the stochastic method of averaging, we show that the stochastic model displays behaviour consistent with that of the underlying deterministic model when the time lag in the formation of the price trends used by the chartists is not too close to zero. However, when this lag approaches zero, such consistency breaks down.

Asset price and wealth dynamics in a financial market with heterogeneous agents

Journal of Economic Dynamics and Control, 2006

This paper considers a discrete-time model of a financial market with one risky asset and one risk-free asset, where the asset price and wealth dynamics are determined by the interaction of two groups of agents, fundamentalists and chartists. In each period each group allocates its wealth between the risky asset and the safe asset according to myopic expected utility maximization, but the two groups have heterogeneous beliefs about the price change over the next period: the chartists are trend extrapolators, while the fundamentalists expect that the price will return to the fundamental. We assume that investors' optimal demand for the risky asset depends on wealth, as a result of CRRA utility. A market maker is assumed to adjust the market price at the end of each trading period, based on excess demand and on changes of the underlying reference price. The model results in a nonlinear discrete-time dynamical system, with growing price and wealth processes, but it is reduced to a stationary system in terms of asset returns and wealth shares of the two groups. It is shown that the longrun market dynamics are highly dependent on the parameters which characterize agents' behaviour as well as on the initial condition. Moreover, for wide ranges of the parameters a (locally) stable fundamental steady state coexists with a stable 'non-fundamental' steady state, or with a stable closed orbit, where only chartists survive in the long run: such cases require the