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23
why stock market crash
, 2003
"... Abstract: The young science of complexity, which studies systems as diverse as the human body, the earth and the universe, offers novel insights on the question raised in the title. The science of complexity explains largescale collective behavior, such as wellfunctioning capitalistic markets, and ..."
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Cited by 51 (11 self)
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Abstract: The young science of complexity, which studies systems as diverse as the human body, the earth and the universe, offers novel insights on the question raised in the title. The science of complexity explains largescale collective behavior, such as wellfunctioning capitalistic markets, and also predicts that financial crashes and depressions are intrinsic properties resulting from the repeated nonlinear interactions between investors. Applying concepts and methods from complex theory and statistical physics, we have developed mathematical measures to successfully predict the emergence and development of speculative bubbles as well as depressions. This essay attempts to capture and extend the essence of the book with the same title published in January 2003 by Princeton University Press. Recent novelties and live predictions are available at
Was There a Nasdaq Bubble in the Late 1990s?
, 2004
"... Not necessarily. The fundamental value of a firm increases with uncertainty about average future profitability, and this uncertainty was unusually high in the late 1990s. We calibrate a stock valuation model that includes this uncertainty, and compute the level of uncertainty that is needed to match ..."
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Cited by 35 (7 self)
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Not necessarily. The fundamental value of a firm increases with uncertainty about average future profitability, and this uncertainty was unusually high in the late 1990s. We calibrate a stock valuation model that includes this uncertainty, and compute the level of uncertainty that is needed to match the observed Nasdaq valuations at their peak. This uncertainty seems plausible because it matches not only the high level but also the high volatility of Nasdaq stock prices. We also show that uncertainty about average profitability has the biggest effect on stock prices when the equity premium is low.
2001) Significance of logperiodic precursors to financial crashes, Quantitative Finance
"... We clarify the status of logperiodicity associated with speculative bubbles preceding financial crashes. In particular, we address Feigenbaum’s [2001] criticism and show how it can be rebuked. Feigenbaum’s main result is as follows: “the hypothesis that the logperiodic component is present in the ..."
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Cited by 34 (16 self)
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We clarify the status of logperiodicity associated with speculative bubbles preceding financial crashes. In particular, we address Feigenbaum’s [2001] criticism and show how it can be rebuked. Feigenbaum’s main result is as follows: “the hypothesis that the logperiodic component is present in the data cannot be rejected at the 95 % confidence level when using all the data prior to the 1987 crash; however, it can be rejected by removing the last year of data. ” (e.g., by removing 15 % of the data closest to the critical point). We stress that it is naive to analyze a critical point phenomenon, i.e., a power law divergence, reliably by removing the most important part of the data closest to the critical point. We also present the history of logperiodicity in the present context explaining its essential features and why it may be important. We offer an extension of the rational expectation bubble model for general and arbitrary riskaversion within the general stochastic discount factor theory. We suggest guidelines for using logperiodicity and explain how to develop and interpret statistical tests of logperiodicity. We discuss the issue of prediction based on our results and the evidence of outliers in the distribution of drawdowns. New statistical tests demonstrate that the 1 % to 10 % quantile of the largest events of the population of drawdowns of the Nasdaq composite index and of the Dow Jones Industrial Average index belong to a distribution significantly different from the rest of the population. This suggests that very large drawdowns result from an amplification mechanism that may make them more predictable than smaller market moves. 1
Asset price bubbles in an incomplete market
, 2007
"... This paper studies asset price bubbles in a continuous time model using the local martingale framework. Providing careful definitions of the asset’s market and fundamental price, we characterize all possible price bubbles in an incomplete market satisfying the ”no free lunch with vanishing risk” and ..."
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Cited by 8 (2 self)
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This paper studies asset price bubbles in a continuous time model using the local martingale framework. Providing careful definitions of the asset’s market and fundamental price, we characterize all possible price bubbles in an incomplete market satisfying the ”no free lunch with vanishing risk” and ”no dominance” assumptions. We propose a new theory for bubble birth which involves a nontrivial modification of the classical framework. We show that the two leading models for bubbles as either charges or as strict local martingales, respectively, are equivalent. Finally, we investigate the pricing of derivative securities in the presence of asset price bubbles, and we show that: (i) European put options can have no bubbles, (ii) European call options and discounted forward prices can have bubbles, but the magnitude of their bubbles must equal the magnitude of the asset’s price bubble, (iii) with no dividends, American call prices must always equal an otherwise identical European call’s price, regardless of bubbles, (iv) European putcall parity in market prices must always hold, regardless of bubbles, and (v) futures price bubbles can exist and they are independent of bubbles in the underlying asset’s price. These results imply that in a market satisfying NFLVR and no dominance, in the presence of an asset price bubble, risk neutral valuation can not be used to match call option prices. We propose, but do not implement, some new tests for the existence of asset price bubbles using derivative securities.
Muzy: Volatility Fingerprints of Large Shocks: Endogeneous Versus Exogeneous arXiv:condmat/0204626
, 2003
"... Finance is about how the continuous stream of news gets incorporated into prices. But not all news have the same impact. Can one distinguish the effects of the Sept. 11, 2001 attack or of the coup against Gorbachev on Aug., 19, 1991 from financial crashes such as Oct. 1987 as well as smaller volatil ..."
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Cited by 5 (4 self)
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Finance is about how the continuous stream of news gets incorporated into prices. But not all news have the same impact. Can one distinguish the effects of the Sept. 11, 2001 attack or of the coup against Gorbachev on Aug., 19, 1991 from financial crashes such as Oct. 1987 as well as smaller volatility bursts? Using a parsimonious autoregressive process with longrange memory defined on the logarithm of the volatility, we predict strikingly different response functions of the price volatility to great external shocks compared to what we term endogeneous shocks, i.e., which result from the cooperative accumulation of many small shocks. These predictions are remarkably wellconfirmed empirically on a hierarchy of volatility shocks. Our theory allows us to classify two classes of events (endogeneous and exogeneous) with specific signatures and characteristic precursors for the endogeneous class. It also explains the origin of endogeneous shocks as the coherent accumulations of tiny bad news, and thus unify all previous explanations of large crashes including Oct. 1987. 1
Slimming” of power law tails by increasing market returns, in press in Quantitative Finance (eprint at http://arXiv.org/abs/condmat/0010112
 Advances in behavioral finance (New York : Russell Sage Foundation
, 2001
"... We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by [20] that the distribution of returns is a power law with exponent less than 1, in contradiction with empirical data. The idea is that the price fluctuations associated with bubbles mus ..."
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Cited by 2 (1 self)
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We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by [20] that the distribution of returns is a power law with exponent less than 1, in contradiction with empirical data. The idea is that the price fluctuations associated with bubbles must on average grow with the mean market return r. When r is larger than the discount rate rδ, the distribution of returns of the observable price, sum of the bubble component and of the fundamental price, exhibits an intermediate tail with an exponent which can be larger than 1. This regime r> rδ corresponds to a generalization of the rational bubble model in which the fundamental price is no more given by the discounted value of future dividends. We explain how this is possible. Our model predicts that, the higher is the market remuneration r above the discount rate, the larger is the power law exponent and thus the thinner is the tail of the distribution of price returns. 1 The fundamental constraint on distribution of returns of rational bubbles Since the publication of the original contributions on rational expectations (RE) bubbles by [3] and [4], a huge literature has emerged on theoretical refinements of the original concept and the empirical detectability of RE bubbles in financial data (see [7] and [1], for surveys of this literature). [4] proposed a model with periodically collapsing bubbles in which the bubble component of the price follows an exponential explosive path (the price being multiplied by at = ā> 1) with probability π and collapses to zero (the price being multiplied by at = 0) with probability 1 − π. It is clear that, in this model, a bubble has an exponential distribution of lifetimes with a finite average lifetime π/(1 − π). Bubbles are thus transient phenomena. In order to allow for the start of new bubble after the collapse, a stochastic zero mean normally distributed component bt is added to the
Strategic behavior and information transmission in a stylized (socalled Chinos) guessing game
, 2000
"... : A guessing game very popular in some European countries involves several players hiding in their hands a number of coins (or pebbles) between zero and three, then attempting to guess in turn the total number of coins in the hands of everyone, with the restriction that no player can repeat the ..."
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: A guessing game very popular in some European countries involves several players hiding in their hands a number of coins (or pebbles) between zero and three, then attempting to guess in turn the total number of coins in the hands of everyone, with the restriction that no player can repeat the guess issued by any predecessor. After a full round, the player, if any, who guesses correctly wins. Of course, rounds without a winner are also possible, in which case a new round is started afresh. The purpose of the present article is to present an analysis of this game (called Chinos in Spain, as a perturbation of \chinas", i.e. pebbles), and some of its possible variants. Our primary aim is to show its potential to shed light on some issues of strategic behavior and information transmission that seem very germane to some social and economic problems. KEYWORDS : Information transmission, herding, Guessing game, Chinos game. 1. Introduction As explained, Chinos is a simple nonc...
(address for correspondence)
, 2005
"... In 1992 a blueribbon group of US economists led by Michael Porter concluded that the US stock marketbased corporate model was misallocating resources and jeopardising US competitiveness. The faster growth of US economy since then and the supposed US lead in the spread of information technology has ..."
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In 1992 a blueribbon group of US economists led by Michael Porter concluded that the US stock marketbased corporate model was misallocating resources and jeopardising US competitiveness. The faster growth of US economy since then and the supposed US lead in the spread of information technology has brought new legitimacy to the stock market and the corporate model, which is being hailed as the universal standard. Two main conclusions of the analysis presented here are: (a) there is no warrant for revising the blueribbon group’s conclusion; and (b) even US corporations let alone developing country ones would be better off not having stock market valuation as a corporate goal.
Speculative Bubbles Dynamics and the Role of Anchoring
"... We investigate the role played by the anchoringandadjustment heuristic in the speculative bubbles dynamics. In order to link anchoring bias and price deviations from fundamental value, we develop a stock market equilibrium model with heterogeneous investors: fundamental investor anchoring to past ..."
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We investigate the role played by the anchoringandadjustment heuristic in the speculative bubbles dynamics. In order to link anchoring bias and price deviations from fundamental value, we develop a stock market equilibrium model with heterogeneous investors: fundamental investor anchoring to past stock market prices and noise traders. The equilibrium model we derive suggests that price is a function of fundamental value, past price, noise and anchoring level. Based on our model, we run a set of Monte Carlo experiments with various anchoring levels: no anchoring, low anchoring and high anchoring. We bring the evidence that large speculative bubbles can only occur when fundamental traders highly anchor to stock market prices. Noise cannot in itself cause such phenomenon. Our findings also suggest that a high anchoring level is consistent with slowly mean reverting bubbles lasting many years.