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34
Institutional investors and stock market volatility
, 2006
"... We present a theory of excess stock market volatility, in which market movements are due to trades by very large institutional investors in relatively illiquid markets. Such trades generate significant spikes in returns and volume, even in the absence of important news about fundamentals. We derive ..."
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Cited by 55 (6 self)
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We present a theory of excess stock market volatility, in which market movements are due to trades by very large institutional investors in relatively illiquid markets. Such trades generate significant spikes in returns and volume, even in the absence of important news about fundamentals. We derive the optimal trading behavior of these investors, which allows us to provide a unified explanation for apparently disconnected empirical regularities in returns, trading volume and investor size. I.
Colloquium: Statistical mechanics of money, wealth, and income
 Review of Modern Physics
"... ar ..."
A Nonlinear SuperExponential Rational Model of Speculative Financial Bubbles
, 2002
"... Abstract: Keeping a basic tenet of economic theory, rational expectations, we model the nonlinear positive feedback between agents in the stock market as an interplay between nonlinearity and multiplicative noise. The derived hyperbolic stochastic finitetime singularity formula transforms a Gaussia ..."
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Cited by 19 (7 self)
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Abstract: Keeping a basic tenet of economic theory, rational expectations, we model the nonlinear positive feedback between agents in the stock market as an interplay between nonlinearity and multiplicative noise. The derived hyperbolic stochastic finitetime singularity formula transforms a Gaussian white noise into a rich time series possessing all the stylized facts of empirical prices, as well as accelerated speculative bubbles preceding crashes. We use the formula to invert the two years of price history prior to the recent crash on the Nasdaq (april 2000) and prior to the crash in the Hong Kong market associated with the Asian crisis in early 1994. These complex price dynamics are captured using only one exponent controlling the explosion, the variance and mean of the underlying random walk. This offers a new and powerful detection Economic structures and financial markets are among the most studied examples of complex systems [1], together with biological and geological networks, which are characterized by the selforganization of macroscopic “emergent ” properties. One such remarkable behavior is the occurrence of intermittent accelerated selfreinforcing behavior [2], such as in the maturation of the motherfetus complex culminating
The exchange rate in a behavioural finance framework
, 2005
"... We develop a simple model of the foreign exchange market in which agents optimize their portfolio and use different forecasting rules. They check the profitability of these rules ex post and select the more profitable one.This model produces two kinds of equilibria, a fundamental and a bubble one. I ..."
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Cited by 15 (5 self)
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We develop a simple model of the foreign exchange market in which agents optimize their portfolio and use different forecasting rules. They check the profitability of these rules ex post and select the more profitable one.This model produces two kinds of equilibria, a fundamental and a bubble one. In a stochastic environment the model generates a complex dynamics in which bubbles and crashes occur at unpredictable moments. We also analyse the empirical relevance of the model 1 1
Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis. URL http://arxiv.org/abs/0905.0220. To appear
 in the Proceedings of APFA7. 16/17
, 2009
"... Abstract The financial crisis of 2008, which started with an initially welldefined epicenter focused on mortgage backed securities (MBS), has been cascading into a global economic recession, whose increasing severity and uncertain duration has led and is continuing to lead to massive losses and dam ..."
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Cited by 14 (6 self)
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Abstract The financial crisis of 2008, which started with an initially welldefined epicenter focused on mortgage backed securities (MBS), has been cascading into a global economic recession, whose increasing severity and uncertain duration has led and is continuing to lead to massive losses and damage for billions of people. Heavy central bank interventions and government spending programs have been launched worldwide and especially in the USA and Europe, with the hope to unfreeze credit and boltster consumption. Here, we present evidence and articulate a general framework that allows one to diagnose the fundamental cause of the unfolding financial and economic crisis: the accumulation of several bubbles and their interplay and mutual reinforcement has led to an illusion of a “perpetual money machine ” allowing financial institutions to extract wealth from an unsustainable artificial process. Taking stock of this diagnostic, we conclude that many of the interventions to address the socalled liquidity crisis and to encourage more consumption are illadvised and even dangerous, given that precautionary reserves were not accumulated in the “good times ” but that huge liabilities were. The most “interesting ” present times constitute unique opportunities but also great challenges, for which we offer a few recommendations.
The Generalized Extreme Value (GEV) Distribution, Implied Tail Index and Option Pricing 1
, 2005
"... Crisis events such as the 1987 stock market crash, the Asian Crisis and the bursting of the DotCom bubble have radically changed the view that extreme events in financial markets have negligible probability. This paper argues that the use of the Generalized Extreme Value (GEV) distribution to model ..."
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Cited by 6 (2 self)
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Crisis events such as the 1987 stock market crash, the Asian Crisis and the bursting of the DotCom bubble have radically changed the view that extreme events in financial markets have negligible probability. This paper argues that the use of the Generalized Extreme Value (GEV) distribution to model the Risk Neutral Density (RND) function provides a flexible framework that captures the negative skewness and excess kurtosis of returns, and also delivers the market implied tail index of asset returns. We obtain an original analytical closed form solution for the Harrison and Pliska (1981) no arbitrage equilibrium price for the European option in the case of GEV asset returns. The GEV based option prices successfully remove the well known pricing bias of the BlackScholes model. We explain how the implied tail index is efficacious at identifying the fat tailed behaviour of losses and hence the left skewness of the price RND functions, particularly around crisis events.
Bubbles and crashes in a behavioural finance model, CESifo Working Paper n°1194
, 2006
"... We develop a simple model of the exchange rate in which agents optimize their portfolio and use different forecasting rules. They check the profitability of these rules ex post and select the more profitable one.This model produces two kinds of equilibria, a fundamental and a bubble one. In a stoch ..."
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Cited by 5 (0 self)
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We develop a simple model of the exchange rate in which agents optimize their portfolio and use different forecasting rules. They check the profitability of these rules ex post and select the more profitable one.This model produces two kinds of equilibria, a fundamental and a bubble one. In a stochastic environment the model generates a complex dynamics in which bubbles and crashes occur at unpredictable moments. We contrast these "behavioural " bubbles with "rational " bubbles.
Empirical distributions of logreturns: Between the stretched exponential and the power law? Quantitative Finance
"... A large consensus now seems to take for granted that the distributions of empirical returns of financial time series are regularly varying, with a tail exponent b close to 3. First, we show by synthetic tests performed on time series with time dependence in the volatility with both Pareto and Stretc ..."
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Cited by 4 (2 self)
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A large consensus now seems to take for granted that the distributions of empirical returns of financial time series are regularly varying, with a tail exponent b close to 3. First, we show by synthetic tests performed on time series with time dependence in the volatility with both Pareto and StretchedExponential distributions that for sample of moderate size, the standard generalized extreme value (GEV) estimator is quite inefficient due to the possibly slow convergence toward the asymptotic theoretical distribution and the existence of biases in presence of dependence between data. Thus it cannot distinguish reliably between rapidly and regularly varying classes of distributions. The Generalized Pareto distribution (GPD) estimator works better, but still lacks power in the presence of strong dependence. Then, we use a parametric representation of the tail of the distributions of returns of 100 years of daily return of the Dow Jones Industrial Average and over 1 years of 5minutes returns of the Nasdaq Composite index, encompassing both a regularly varying distribution in one limit of the parameters and rapidly varying distributions of the class of the StretchedExponential (SE) and LogWeibull distributions in other limits. Using the method of nested hypothesis testing (Wilks ’ theorem),
Quantifying Herding During Speculative Financial Bubbles, preprint at http://arXiv.org/abs/condmat /0104341
 Technometrics
, 2001
"... Economic structures and financial markets are among the most studied examples of complex systems [1], together with biological and geological networks, which are characterized by the selforganization of macroscopic “emergent ” properties. One such remarkable behavior is the occurrence of intermitte ..."
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Cited by 3 (3 self)
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Economic structures and financial markets are among the most studied examples of complex systems [1], together with biological and geological networks, which are characterized by the selforganization of macroscopic “emergent ” properties. One such remarkable behavior is the occurrence of intermittent accelerated selfreinforcing behavior, such as in the maturation of the motherfetus complex culminating in parturition [2], in the observed accelerated seismicity ending in a great earthquake [3], in positivefeedbacks in technology (Betamax versus VHS video standards) [4] or in the herding of speculators preceeding crashes [5]. Keeping a basic tenet of economic theory, rational expectations, we model the nonlinear positive feedback between agents as an interplay between nonlinearity and multiplicative noise. The derived hyperbolic stochastic finitetime singularity formula transforms a Gaussian white noise into a rich time series possessing all the stylized facts of empirical prices and more, i.e., no correlation of returns [6], longrange correlation of volatilities [7], fattail of return distributions [8, 9, 10], apparent multifractality [11, 12], sharp peakflat trough pattern of price peaks [13] as well as accelerated speculative bubbles preceding crashes [5]. We use the formula to invert the two years of price history prior to the recent crash on the Nasdaq (april 2000) and prior to the crash in the Hong Kong market associated with the Asian crisis in early 1994. These complex price dynamics are captured using only one exponent controlling the explosion, the variance and mean of the underlying random walk. This offers a
Diagnostics of Rational Expectation Financial Bubbles with Stochastic MeanReverting Termination Times
"... We propose two rational expectation models of transient financial bubbles with heterogeneous arbitrageurs and positive feedbacks leading to selfreinforcing transient stochastic fasterthanexponential price dynamics. As a result of the nonlinear feedbacks, the termination of a bubble is found to ..."
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Cited by 2 (1 self)
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We propose two rational expectation models of transient financial bubbles with heterogeneous arbitrageurs and positive feedbacks leading to selfreinforcing transient stochastic fasterthanexponential price dynamics. As a result of the nonlinear feedbacks, the termination of a bubble is found to be characterized by a finitetime singularity in the bubble price formation process ending at some potential critical time t̃c, which follows a meanreversing stationary dynamics. Because of the heterogeneity of the rational agents’ expectations, there is a synchronization problem for the optimal exit times determined by these arbitrageurs, which leads to the survival of the bubble almost all the way to its theoretical end time. The explicit exact analytical solutions of the two models provide nonlinear transformations which allow us to develop novel tests for the presence of bubbles in financial time series. Avoiding the difficult problem of parameter estimation of the stochastic differential equation describing the price dynamics, the derived operational procedures allow us to diagnose bubbles that are in the making and to forecast their termination time. The tests performed on three financial markets, the US S&P500 index from