Reflexivity, Coherent Markets, and Financial Instability:

Reconsidering Alternative Explanations for Departures from Generally Accepted Economic and Financial Theory

J. Douglas Barrett
Professor of Quantitative Methods and Chair
Department of Economics and Finance
University of North Alabama
Florence, AL 35632
jdbarrett@una.edu

Peter M. Williams
Professor of Economics
Department of Economics and Finance
University of North Alabama
Florence, AL 35632
pmwilliams@una.edu


ABSTRACT

The current financial crisis has caused a reassessment of many canonical assumptions underpinning traditional theory in economics and finance.  Specifically, the real estate and financial markets have exhibited behavior that belies previously expected conditions.  Nonstandard theories have existed for decades, but have been largely ignored by mainstream academia.  The Reflexivity Theory of Soros, the Coherent Markets Hypothesis of Vaga, and the Financial Instability Hypothesis of Minsky are three potentially viable theories.  The current work is an investigation of these and other alternative theories in economic and financial analysis.


INTRODUCTION

Traditionally, the dominant school of thought in finance is the Efficient Market
Hypothesis (EMH).  (See, e.g., [3].)  In its simplest form, the EMH asserts that market prices reflect all available information.  Theoretically based in mathematics, the EMH is the foundation for much of the inquiry in the discipline.  Empirical studies have shown results that are, at best, mixed.  The recent economic crisis has exacerbated the situation.

The EMH is based on several assumptions.  It asserts that past information does not affect market activity (i.e., the process is “memoryless”), once this information is generally known.  Another assumption is that capital market behavior follows a “random walk.”  Furthermore, with a sufficiently large sample, the returns become well approximated by a normal (Gaussian) distribution.

The purpose of the current study is to discuss issues with the EMH, and highlight the current alternative theories.  In the next section, empirical departures from the aforementioned assumptions for the EMH are discussed.  The succeeding section highlights the list of alternative theories, with a brief description of each.  The paper concludes with a summary and points of convergence for the competing theories.  ...

download pdf of complete paper at:

http://rwahlers.iweb.bsu.edu/abd2009/Papers/p09_barrett_williams.pdf

Social Imitation Modell

Social Imitation Modell

Ulf A. Hamster 

Erste Version: 23. März 2009, Aktuell: 14. Juni 2009

Zusammenfassung

Das Ising Modell wird als Markov-Ketten Modell implementiert, was exogen über den Crowding- und Fundamentalverzerrungsparameter gesteuert werden kann, um eine bimodale Verteilung bezüglich der Kaufodere Verkaufsneigung der Agenten zu erzeugen.

1 Einleitung

Coherent Market Hypothesis. Der Aspekt sich gegenseitig beeinflussen- der Agenten wird in der Coherent Market Hypothese (CMH) nach Vaga (1990) aufgegriffen. Die CMH differenziert zwischen effizienten, kohärenten trend- behafteten, chaotischen, instabilen und zurücktreibenden Marktphasen (Schöbel und Veith, 2006, S. 6), welche über die Parameter einer bimodalen Verteilung modelliert wird (Tab. 1). Während Vaga (1990) von einer Renditever- teilung ausgeht, wird i.d.R. die Wahrscheinlichkeit der Anzahl nachfragender vs. anbietender Marktteilnehmer aufgrund gegenseitiger Imitation betrachtet. Wie Shmatov und Smirnov (2005) zeigen, kann letzteres mit Hilfe von Markov-Ketten numerisch implementiert werden (Kap.2).

Interaktion zwischen Agenten. Methodischer Ausgangspunkt ist das Ising Modell zur Beschreibung von Ferromagnetismus, das analog Interaktions- möglichkeiten auf benachbahrte Agenten einschränkt, z.B. Iori (2002) und Sornette und Zhou (2006). Als qualitative Begründungen können Erkenntnisse nicht assozierter empirischer Studien bezüglich Finanzmarktentscheidungen herangezogen werden, z.B. Mund zu Mund Effekt (Hong u. a., 2004, 2005; Brown u. a., 2008), Home Bias Effekt (Huberman, 2001; Massa und Simonov, 2006), und Lokaler Informationsvorteil (Coval und Moskowitz, 2001, 1999; Ivkovic und Weisbenner, 2005), welche als Verkettung von Fehler indi- vidueller Verfügbarkeitsheuristiken (Kuran und Sunstein, 1999) interpretiert werden können.

Heterogene Agenten. Jedoch vernachlässigt das Iori/Ising-Modell wie viele Agenten was tun und wie sie sich gegenseitig beeinflussen, z.B. Unterscheidung der Noise Trader von Fundamentalanlysten (Lux, 1995, 1997), Strate- giewechsel und Markteintritt- & austritt von Agenten (Lux, 1998, S. 149ff.), der Einfluss der Gesamtanzahl der Agenten im Markt (Egenter u. a., 1999), oder individuelle Selbsttäuschung wie Optimismus & Pessimismus (Chen u. a., 2001) Obwohl die Iori-Modelle durch die Nächste Nachbar Einschränkung eine Verfügbarkeitsheuristik impliziert, bilden Lux-Marchesi-Modelle empirische Eigenschaften von Finanzmarktreihen besser ab und sind diesbe- züglich plausibler begründet.

Alzheimer Random Walks and Market Bubbles?

Analytic Formulation, Exact Solutions, and Generalizations of the Elephant and the Alzheimer Random Walks

V. M. Kenkre

An analytic formulation of memory-possessing random walks introduced recently [Cressoni et al., Phys. Rev. Lett. 98, 070603 (2007) and Sch\"utz and Trimper, Phys. Rev. E 70, 045101 (2004)] for Alzheimer behavior and related phenomena is provided along with exact solutions on the basis of Fokker-Planck equations. The solution of a delay-differential equation derived for the purpose is shown to produce log-periodic oscillations and to coincide rather accurately with previously published computer simulation results. Generalizations along several directions are also constructed on the basis of the formalism.

Two remarkable publications have recently appeared on the subject of random walks with memory, one in- volving the ‘elephant walk’ in which the walker chooses steps randomly but is influenced by a perfect memory of steps taken earlier [1], and the other involving an extension of this walk to incorporate partial memory of steps from the beginning up to a time in the past [2]. While an analytical description has been given for the (former) elephant walk, it appears to have been impossible to provide one for the partial memory extension. The significance of the latter is that it has been proposed [2] for the medically important analysis of amnestically in- duced behavior of Alzheimer patients. The authors of Ref. [2] have presented impressive computer simulations of the Alzheimer walk exhibiting log-periodic oscillations in the displacement of the walker, and deduced intriguing conclusions regarding the elements of persistence and what they have called, following Schu ̈tz and Trimper [1], traditional versus reformer behavior of the walker. They have also stated that an analytic solution of their partial memory extension (the Alzheimer walk) remains an open problem. The present Letter is aimed at solving that problem. 

The quote above is from an interesting paper on random walks with either perfect memory (elephant walks) or memory of the past without recent memory (Alzheimer's walks). The latter is given an analytic treatment based on a time dependent Fokker Planck Equation. This is of interest for two reasons: 1. our Coherent Market Hypothesis (CMH) is based on the Fokker Planck Equation; and 2. The log periodic oscillations that occur with Alzheimer's random walks have empirically been found to be precursors to market bubbles and crashes (or at least regime changes) by Didier Sornette, et. al.

The CMH is based on a stationary (time independent) Fokker Planck Equation. Therefore this paper by V. M. Kenkre paves the way for introducing time dependence into the CMH formalism leading to prediction of log periodic oscillations in the financial markets. Clearly this is an important opportunity for research on extending the CMH into time dependent as well as stationary state dynamics.

RELATIVISTIC QUANTUM ECONOPHYSICS – NEW PARADIGMS IN COMPLEX SYSTEMS MODELLING V. Saptsin and V. Soloviev

"Econophysics, or physical economics, already mentioned as a relatively young scientific school, recently celebrated its tenth anniversary. Of course that doesn’t mean that there were no works on the boundary of economics and physics before the econophysics was officially born, howewer the new direction is usually formed only when the certain conditions appear and the necessity to concentrate the scientific forces arises. Quantum econophysics is not an exception. That is why, though the first work according to Gonsales [18], which can be related to the application of quantum mechanical ideas to the economic phenomena, appeared in 1990 [55], we can speak about the birth of the new scientific direction called econophysics only nowadays."

[18] C. P. Goncalves, An Evolutionary Quantum Game Model of Financial Market Dynamics - Theory and Evidence, April 14, 2007, URL http://ma.utexas.edu/mp arc/c/07/07- 89.pdf .

[55] T. Vaga, The Coherent Market Hypothesis, Financial Analysts Journal, November/December, 36–49 ( 1990).

ETH Zurich Workshop Presentation: A Financial Market Bifurcation Parameter

Can financial market crises be predicted? We propose a Bifurcation Parameter in this regard.


BACKGROUND: Weidlich proposes the Ising Model to describe polarization of opinions in social groups. Haken's model includes the Langevin equation of Brownian motion as a special case and references Weidlich's work as an example of more ordered states in social systems. Vaga applies Weidlich and Haken's state transition concepts to formulate the Coherent Market Hypothesis. Vaga and Nawrocki develop a novel bifurcation parameter and analyze coherent, chaotic, efficient and disordered (crisis) market states.


The Coherent Market Hypothesis provides the theoretical basis for defining a quantitative bifurcation parameter, a potential indicator crisis situations in the financial markets.


The empirical daily conditional return map from 1929 to present illustrates bullish and bearish equilibrium states (where the return map crosses zero). The slope of the conditional return map in the neighborhood of moderate returns is positive with high statistical significance.


The slope of the conditional return (CR) map governs the bifurcation process from the linear, disordered state to the more structured bull and bear states.


The bifurcation parameter is the 200 day sum of conditional returns after moderate positive returns minus the 200 day sum of conditional returns after moderate negative returns. This parameter is related to the slope of the CR map.


The Bifurcation Parameter (BP) has dropped well below -10% in crisis markets such the Crash of 1929 and Great Depression Era. In contrast, the BP didn't drop below -10% at all in the post WW II Era (1946-1975). Since the advent of computerized trading and negotiated commissions in the mid-1970s, the BP has indicated a more efficient market, though recently this indicator has fallen to levels not seen since the Great Depression Era.


In the 1929 to 1939 period, the bifurcation parameter fell well below -10% and remained there on three occasions, each of which resulted in significant market declines


In the 1999 to 2009 period there were two large declines in the Bifurcation Parameter below -10%, one coincided with rising stock prices and the other with a large decline to date.


Periods with a negative BP have a significant negative bias in the conditional return map.


Periods with a BP greater than +10% have a higher degree of bull and bear trend persistence.


Market state definitions can be based solely on the Bifurcation Parameter.


Ordered markets, including both coherent and chaotic states, outperform efficient market periods, while disordered (crisis) markets have underperformed by a large degree.


Ordered markets can be decomposed into coherent bull markets (when the prior day return is >0) or chaotic markets when the prior day return is negative.


Coherent, chaotic, efficient and crisis markets have widely varying risk and reward profiles.


The Crash of 1929 and Great Depression Era was highly volatile.


The post World War II Era enjoyed a high degree of trend persistent, coherent and chaotic markets.


Since the advent of negotiated commissions in 1975, the markets have become more efficient on average.


Returns in coherent and chaotic markets are highly statistically significant. Disordered markets (mean regressive reversals after positive returns) are also statistically significant. However due to the high volatility and relatively limited amount of data, crisis market returns are only significant to the 90% level.


The Bifurcation Parameter provides a statistically significant indicator of the coherent and chaotic market states predicted by the Coherent Market Hypothesis. However, due to the extreme volatility and limited number of crisis markets the significance of this state has only been partially established, i.e. reversals of prior day price advances.




BACKUP CHARTS



The NASDAQ Composite Index exhibited a high degree of coherence from 1971 through the year 2000. It is currently in a disordered state.



The S&P500 Index has exhibited large upside reversals in the recent mean regressive market.

Over Reaction, Disordered Market Continues

We introduce an Efficient Market state, defined as -10% < Bifurcation Parameter < +10%. This represents a market where there isn't much over reaction or under reaction to news. We also update prior coherent and chaotic market state definitions, requiring the Bifurcation Parameter to be >= +10%. Therefore the Coherent and Chaotic markets clearly represent under reaction situations and trend persistent states. We also use the prior day return, R(t) to differentiate between coherent (R(t)>=0) and chaotic (R(t)<0) states. These definitions and associated risk and returns since July 1929 are summmarized as follows:

Coherent Bull Markets
Bifurcation Parameter >= +10%
R(t) >= 0 (prior day return is positive)
RETURN 37.94%
RISK 15.05%
% TIME 24.16%

Efficient Markets
-10% < Bifurcation Parameter < +10%
RETURN 6.16%
RISK 14.85%
% TIME 45.25%

Chaotic Markets
Bifurcation Parameter > +10%
R(t) < 0 (prior day return is negative)
RETURN -13.50%
RISK 17.87%
% TIME 22.15%

Disordered Markets
Bifurcation Parameter < -10%
RETURN -17.17%
RISK 36.65%
% TIME 8.43%

CURRENT MARKET: DISORDERED STATE

(click on image to expand)

During the past 12 months the Dow Industrials have had an even lower return and higher risk than the average for prior extremely disordered markets. The high volatility of extremely disordered markets includes large swings both up and down. While the stimulus and bailout programs should provide the credit necessary to eventually restore normal market structure, so far the quantitative evidence is consistent with a disordered market state.

Chaos theory and the current financial crisis

Years ago, in a letter to the editor of Physics Today (February, 1979) we noted that the “market may be considered an open system in which an adequate flow of money will effect a transition from disorder (random walk) to order (cooperative or crowd behavior).” Open systems in the physical sciences require a flow of energy to maintain an ordered state far from thermal equilibrium. For example, a laser requires energy to be pumped continuously to maintain a coherent state. In the financial markets, price stability requires a flow of money or credit. In the Great Depression, credit became scarce as the bubble in stock prices unwound after the "Roaring Twenties." The current credit crisis involves the unwinding of the housing bubble and associated derivative securities.

We define a market “attractor” as a conditional return map, i.e. the average return on the day after a prior day return, R(T-1), that falls into one of five intervals:


small price changes [-0.5% < R(T-1) < +0.5%]
moderate price increases [+0.5% < R(T-1) < +3.5%]
moderate price declines [-0.5% > R(T-1) > -3.5%]
large price increase [+3.5% < R(T-1)]
large price declines [-3.5%] > R(T-1)]

Figure 1 summarizes the average conditional return map for the Dow Jones Industrial Average over the 80 year period from 1929 to 2009. A nonlinear third order polynomial fit is shown and illustrates that the market has been trend persistent on average over this period. The slope of the return map is positive in the region of moderate returns.


Figure 1. Over the past eighty years the Dow Jones Industrial Average has been governed on average by a coherent, trend persistent dynamic.

The conditional return map in Figure 1 illustrates a bistable attractor for the market. Moderate positive returns are followed on average by further positive returns. Similarly, moderate negative returns are followed on average by further negative returns. These drifts are toward dynamic equilibrium points (where the return map crosses zero) far from the market’s long term average daily return.

Next, we identify state transitions from a mean regressive market attractor to a bistable state attractor. First we define a bifurcation parameter as the sum over 200 days of conditional returns following moderate price increases (as defined above), minus the sum over 200 days of conditional returns after moderate price declines. In a mean regressive market, where the return map has a negative slope, this metric is negative whereas in a trend persistent market it is positive. The market attractor bifurcates as this measure crosses zero.

The bifurcation parameter is plotted in Figure 2. The most significant mean regressive markets occurred in the Great Depression era of the 1930s, though there were some wild swings in this indicator. From the 1940s to about 1980, the market was primarily in a trend persistent state and fluctuations of the bifurcation parameter were primarily around a positive mean. The further the bifurcation parameter deviates from zero, the better the opportunities for short term trading: in the Great Depression era a mean reversion strategy would have offered the best chance for success; from 1940 to 1980, a trend following strategy had the odds in its favor. However, more recently with the advent of computerized trading and negotiated commissions, the market has become more efficient, with less opportunity for trading.


Figure 2. The bifurcation parameter is negative in mean reverting market states and positive in trend persistent coherent markets, reflecting the slope of the conditional return map for moderate returns.


Figure 3 illustrates the market return map or attractor for market periods between 1929 and 2009 when the bifurcation parameter is negative. In this situation, moderate positive returns are followed on average by negative returns on the following day; moderate negative returns are followed by positive returns on average.


Figure 3. The market is mean regressive when the slope of the conditional return map and the bifurcation parameter are negative.

Recently the bifurcation parameter has dropped deeply into negative territory. This is an unusual development since this indicator hasn’t fallen this far since the Great Depression era. A short term trading strategy designed to profit from the market’s regression to the mean after moderate returns is appropriate in this market state. A strategy of avoiding equity positions entirely when the bifurcation parameter drops below -10% is illustrated in Figure 4. This straategy would have outperformed a buy and hold both in the Crash of 1929 and also successfully avoided much of the recent market meltdown. However, there is no assurance as to how it will work in the future particularly as it is based on a lagging indicator of market dynamics.


Figure 4. Avoiding mean reverting markets (negative bifurcation parameter) has shown profitable back testing results, but may not work in future markets.

Nonlinear and Chaotic Dynamics and its Application to Historical Financial Markets

Hartmut Kiehling*

For complete article click here.

Abstract: For roughly 15 years, economic research has been involved with chaotic systems. During these years chaos theory took a firm place in science, although the enthusiasm of the first decade was followed by a more subdued kind of consideration. This might be the time to sum up some of the results and to develop some ideas concerning possible applications of chaos theory to economic history (and its theory). Since a good portion of the chaos research that has been done until now deals with financial markets, we will consider that section of economics.

* Address all communications to Hartmut Kiehling, Heerstraße 9, D-81247 München,
Tel. +49-(0)89-8116379, Fax. +49-(0)89-8110189, e-mail: 101520.2007@compu-serve.com, 0898110189@t-online.de.

T. Vaga published his Coherent Market Hypothesis as a nonlinear statistical model. He distinguishes four market phases: random walk, transition, chaotic markets, and coherent markets. Each one is characterized by different kinds of attitudes and the mutual influence of investors. The model follows the psychological theory of social imitation, but is formulated mathematically. 15

Portfolio optimization with a neural network implementation of the coherent market hypothesis

Manfred Steiner and Hans-Georg Wittkemper

Westfälische Wilhelms-Universität Munster, Lehrstuhl für Betriebswirtschaftslehre, Schwerpunkt Finanzierung, Am Stadtgraben 13–15, D-48143, Münster, Germany

Abstract

Capital market research seems to be widely governed by traditional static linear models like arbitrage pricing theory and capital asset pricing model, though there is some evidence that better results can be achieved using nonlinear approaches. In this study we described a portfolio optimization model based on artificial neural networks embedded in the framework of a nonlinear dynamic capital market model, the coherent market hypothesis. The main advantage of this theory is that it drops the premise of rational investors and therefore relaxes the precondition of approximately normally distributed stock returns. Neural networks are used to estimate the return distributions in order to forecast the fundamental situation and the level of group behavior of the specific stocks. On the basis of these forecasts the relative stock performance is predicted and used to manage stock portfolios, In a simulation with out-of-sample data from 1991–1994 a portfolio constructed from the eight best ranked stocks achieved an annual return rate about 25% higher than that of the market portfolio and one built from the eight worst ranked stocks attained a return about 25% lower than the market portfolio's return rate. A hedging strategy based on the two aforementioned portfolios leads to a consistently positive annual return of about 25% regardless of the movements of the market portfolio with only 41% of the risk of a buy and hold strategy in the market portfolio.

Advanced School of Economics Ca’ Foscari_University of Venice

Exploring Information Mirages
in a Simulated Multi‐Agent Stock Market


Paolo Tasca

Advanced School of Economics, Ca’ Foscari University of Venice
Visiting Fellow Chair of Systems Design, ETH Zürich

First Draft: September 2008

For complete paper click here.

1. Introduction

In this paper we analyze the financial price dynamics emerging from the heterogeneous behaviours of traders interacting in an experimental asset market in presence of asymmetric information. The understanding of the behavior of partially informed agents in experimental settings is a critical step toward understanding behavior in real markets.

Access to qualitative private information gives the traders the opportunity to exploit a dominant position when trading with uninformed agents. This in turn motivates not only the search for information but also the communication of misleading information. For the uninformed traders, a situation of general uncertainty may also lead to imitation and ultimately to herding behaviour. As Grossman (1976) has observed, when confidence in fundamentals disappears, naive imitative behaviour may actually be the best option.

According to the theories of information aggregation (Grossman 1976, 1981; Grossman and Stiglitz 1980; Jordan 1982; Diamond and Verecchia 1981; Verecchia 1982), traders have and use different information about the value of assets and through the process of their aggregation, market prices effectively reveal all the information present in the market. Then, in equilibrium traders cannot learn nothing more than prices. In line with the rational expectations (RE) hypothesis, aggregation of diverse information is in general difficult because no single agent possesses full information. Traders can identify the state of nature with certainty only by sharing their individual information in the process of trading. Plott & Sunder (1982) and Forsythe, Palfrey & Plott (1982) study markets with insiders and uninformed traders. They show that the equilibrium prices do reveal insider information after repetition of experiments and conclude that the markets disseminate information efficiently. Plott & Sunder (1982) further show that convergence to the rational expectation equilibrium (REE) occurs in markets that pays diverse dividends to different traders. They attribute the success of the RE model to the fact that traders learn about the equilibrium price and the state simultaneously from market conditions. The results by Plott & Sunder (1988) and Forsythe & Lundholm (1990), on the other hand, show that a market aggregates diverse information efficiently only under certain conditions: identical preferences, common knowledge of the dividend structure, complete contingent claims. These studies provide examples of failure of the RE model and suggest that information aggregation is a more complicated situation. In another related study, O'Brien & Srivastava (1991) find that market efficiency in terms of full information aggregation depends on complexity of the market. In particular, complexity is induced by market parameters such as the number of stocks and the number of periods in the markets.

In a variety of situations the market may actually fail to aggregate information correctly. Salient reasons are information mirages and bubbles (see Camerer C. 1989, Camerer C. and Weigelt, 1991), information traps (see Nöth et al., 1999), and pricemanipulations (see Veiga and Vorsatz, 2008).

In this paper we investigate whether, in a market composed by informed and uninformed agents, uninformed agents may overreact to uninformative trades during the process of information aggregation. Once an agent occurs in such a mistake, she may trade as informed trader causing other traders to wrongly infer that she is an insiders. The misleading path of market prices resulting from such mistakes is what Camerer and Weigelt (1991) has referred to be “price mirages” because prices reveal information which is not really there. Information mirages is an important phenomenon to be analyzed as one explicative cause of some well known stylized facts in financial markets such as excess volatility (Shiller R.J., 1981). As Fisher Black (1986), French and Roll (1984) have considered, volatility of asset prices may be induced by traders overreaction to trades that are not informative, creating self-generated information mirages. We can imagine for example that just by chance, in the first daily trading sessions the most part of the orders are on the sell side. Uninformed traders entering the market later, may reasonable infer that the market sentiment is negative and may be induced to sell. Thus the market price should fall. Others uninformed traders who pay attention on the recent price path may be attracted by the price drop and be induced to enter the market on the sell side as well. This cycle exactly describe what we mean by an information mirage: a sort of mini-bubble which is typically temporary, and possibly small in size. Imitative behaviour may be responsible for a significant proportion of the price volatility observable in real-world asset markets: in inferring information from the trades of others, traders sometimes go wrong and their errors cause others to overreact, creating price paths that falsely reveal information that no one has.

Previous studies (e.g. Camerer and Weigelt, 1991) consider the dynamics of price mirages in the short run (few minutes). Whereas, in this paper we will analyse this phenomenon in the long run (around 1200 trading days): a sufficiently large horizon during which mini-bubbles may grow into big-bubbles.

2. Artificial Financial Market with Noisy and Insider Traders

Information mirages are difficult to detect in natural data because researchers usually do not know what information traders had at any point in time, so it is difficult to know whether prices incorporate all information or not. Instead, in the artificial financial market introduced here we model the flow through which information enter the market allowing the existence of asymmetric information. This arise the problem of what Fischer Black (1986) has referred to as noise trading:

“Noise trading is trading on noise as if it were information. People who trade on noise are willing to trade even though from an objective point of view they would be better off not trading. Perhaps they think the noise they are trading on is information. Or perhaps they just like to trade” (Black F., 1986, p.531)

The experimental approach is ideally suited to investigations of this kind, since it is possible to control both the structure of the market and the signals through which information is disseminated. Two classes of investors will be allow to trade contemporaneously in the market: insider traders and noisy traders. Insider traders, quickly will trade on the received unbiased signals revealing the variation of asset’s true fundamental value. While, noisy traders will behave as boundedly rational agents. They will trade upon indications of external biased signals and will be influenced by other investors’ sentiments. This lead us away from the Efficient Market Hypothesis (EMH) towards the Adaptive Market Hypothesis (AMH)1 and Coherent Market Hypothesis (CMH) of Vaga T. (1990) through the theory of social imitation (Callen,
Shapiro 1974) and the Ising model.

Market prices will be the product of the interplay between insider traders (called “rational arbitrageurs” in Shiller model, 1984) and noisy traders operating under different decision rules. With continuous information flows, the model encourage the interchange of the role between insiders and noisy traders. Insiders, making ex ante rational trades may nevertheless lose money ex post on any given trade. In real financial markets, investors may trade on the right side of the market performing as insider once they receive the right signal. But they can frequently be engaged in noise trades when receiving signals not carrying the true state of nature.

We frame the model into two classes of rules: microstructure rules and behavioral rules. Microstructure rules are all those ones describing the system design and the mechanisms characterizing the functionality of the market. Behavioral rules instead, describe the agents decisions models.

HIPÓTESIS DEL MERCADO COHERENTE

CARACTERÍSTICAS

La HMC fue desarrollada por Vaga (1990) y explica que elmercado puede presentartransiciones de un estado depaseo aleatorio (desordenado)a periodos de comportamientoen masa como en los mercadoscoherentes y caóticos (ordenados). Cerca del umbral críticode transición, el mercado esaltamente susceptible al ruido(noticias de política o deaspectos económicos aleatorios). Así, los mercados vistosa través de la HMC representansistemas complejos 8 y une a lasdos hipótesis vistas ante-riormente: en ocasiones el mercado se podría comportar deforma caótica y en otrassituaciones podría evolucionarde forma aleatoria.

An Overreaction Implementation of the Coherent Market Hypothesis and Option Pricing

RAINER SCHOEBEL
University of Tuebingen - Faculty of Economics and Business Administration
JOCHEN VEITH
University of Tuebingen - Faculty of Economics and Business Administration

Inspired by the theory of social imitation (Weidlich 1970) and its adaptation to financial markets by the Coherent Market Hypothesis (Vaga 1990), we present a behavioral model of stock prices that supports the overreaction hypothesis. Using our dynamic stock price model, we develop a two factor general equilibrium model for pricing derivative securities. The two factors of our model are the stock price and a market polarization variable which determines the level of overreaction. We consider three kinds of market scenarios: Risk-neutral investors, representative Bernoulli investors and myopic Bernoulli investors. In case of the latter two, risk premia provide that herding as well as contrarian investor behaviour may be rationally explained and justified in equilibrium. Applying Monte Carlo methods, we examine the pricing of European call options. We show that option prices depend significantly on the level of overreaction, regardless of prevailing risk preferences: Downward overreaction leads to high option prices and upward overreaction results in low option prices.

Capital Market Theory: Is It Relevant to Practitioners?

David Nawrocki
Villanova University

A more complete theory is Vaga’s(1990) coherent market theory. Vaga argues that the market is constantly changing over time and is a time-varying process. As technology, investor expectations, government policy variables and rate of financialinnovation change, the market can experience different states -- steady state random walk, coherent cycles, and chaotic dynamics. Statistics may be used to describe Vaga’s market states. The random walk has stable symmetric (normal) distributions. The coherent cycle stage has stable skewed (nonnormal) distributions. The chaotic state has unstable skewed distributions. What are the implications? A stable probability distribution (random walk and coherent markets) will exhibit persistence over time. In other words, the distribution provides reasonable expectations of future performance. In addition, a coherent market is going to exhibit regularities that make the market forecastable with simple models. An unstable chaotic distribution implies that simple models cannot forecast the future.

Studying Vaga’s market states provides the interesting insight that his states relate to the business cycle. Vaga’s approach is statistical. However, the business cycle can be approached from an economics perspective. Hunt (1987) and Stovall (1996) have done interesting work on the stock market and the business cycle. Both authors divide the business cycle into different phases. We can divide the business cycle into four phases with each phase corresponding to one of Vaga’s market states. Four possible states of the business cycle are:

1. Easeoff -- The Federal Reserve is trying to cool down a rapidly growing economy that is experiencing increasing rates of inflation. The rate of economic growth slows and reaches a peak in economic activity. Interest rates peak.

2. Plunge -- The Federal Reserve’s anti-inflation policies cause a decline in economic activity (recession). A bottom (trough) occurs during this period. Interest rates and inflation decline during this period.

3. Revival -- The economy starts a recovery with strong economic growth, low inflation and low interest rates.

4. Accelerate -- The economy continues strong growth, however, capacity utilization starts to reach its limits and the economy overheats increasing the inflation rate.

An Evolutionary Quantum Game Model of Financial Market Dynamics - Theory and Evidence

Carlos Pedro Goncalves
Carlos Goncalves

The development of models that generate multifractal patterns in a bottom-up fashion is necessary, both for financial theorists and financial agents. The presence of multifractal patterns makes the markets more risky than predicted by standard financial models, which means that financial agents need to have models that are able to provide for guiding tools in asset and risk management.

Within standard financial theory the multifractal behavior remains unexplained. The development of a model capable of explaining the presence of multifractal signatures in the markets would be a first step towards a financial theory of market dynamics. However, such a model, and such a theory cannot be found in the framework of standard finance.

It has become necessary to review the microscopic assumptions that form the basis for classical finance, where, by microscopic assumptions, we mean the individual agent’s behavior and the interaction rules between agents.

Mathematical physics, and econophysics have provided for competing fields of research where it is possible to study market dynamics from the perspective of microscopic modelling. Spin glasses provide for the oldest examples of the application of physical models to solve unexplained empirical facts in market dynamics. One of the early applications of these models dates back to Vaga’s (1990) coherent market hypothesis, that tried to relate market dynamics to different phases, in an analogy with the different phases of a spin glass.

Although spin glasses have been an example of a simple and effective modelling tool to build microscopic theories of market dynamics, one still lacked a robust model capable of generating self-organized multifractality, until a recent work by Sornette and Zhou (Sornette and Zhou, 2005; Zhou and Sornette 2005, 2007), in which multifractal structure is diagnosed, not only by the standard convexity of the structure functions’ exponents, but also by a continuous spectrum of power law response functions to endogenous shocks.

Self-Organized Criticality in Synchronized Loss Dynamics - A Behavioral Account

Carlos Pedro S. Goncalves
ISCTE − Business School
Miguel A. Ferreira
ISCTE - Business School

Behavioral science and finance are the common element behind the different approaches to artificial financial markets. However, we can divide these approaches in two major branches, one is the branch that stems from a biological framework of analysis and, the other, is the branch that stems from a physical framework.

Although these two branches may be present in a given model, we usually find the presence of one or the other as dominant. For instance, the Santa Fe Artificial Financial Market combines behavioral finance and economics with genetic algorithms that are learning algorithms with a largely biological nature.

Goncalves (2004) artificial financial market, on the other hand, was largely influenced by the physical line of research. In particular, by Doyne Farmer’s work on agent-based modelling and econophysics, Sornette’s work in econophysics (in the modelling of financial crashes), Vaga’s coherent market hypothesis and the synergetics approach to complexity.

Artificial Financial Market

Carlos Pedro Goncalves

WHAT IS IT?

This is a model of an artificial financial market with heterogeneous boundedly rational agents that are influenced by the sentiment of their most close colleagues regarding the future evolution of the market.

The model is capable of generating the stylized facts of the real financial markets, specifically: excess volatility in the logarithmic returns, clustered volatility (characteristic of the well known GARCH signatures), bubbles and crashes.

The main influences behind this model were Vaga's coherent market hypothesis (Vaga, 1990) and Johansen, Ledoit, Sornette's model (Johansen et. al., 2002, Sornette, 2003), from now on denoted by JLS.

Our model may also be of interest to areas outside of finance, areas like, for instance, the study of social influence, opinion making and political decision.