INEFFICIENT BUBBLES AND EFFICIENT DRAWDOWNS IN FINANCIAL MARKETS

At odds with the common “rational expectations” framework for bubbles, economists like Hyman Minsky, Charles Kindleberger and Robert Shiller have documented that irrational behavior, ambiguous information or certain limits to arbitrage are essential drivers for bubble phenomena and financial crises. Following this understanding that asset price bubbles are generated by market failures, we present a framework for explosive semimartingales that is based on the antagonistic combination of (i) an excessive, unstable pre-crash process and (ii) a drawdown starting at some random time. This unifying framework allows one to accommodate and compare many discrete and continuous time bubble models in the literature that feature such market inefficiencies. Moreover, it significantly extends the range of feasible asset price processes during times of financial speculation and frenzy and provides a strong theoretical background for future model design in financial and risk management problem settings. This conception of bubbles also allows us to elucidate the status of rational expectation bubbles, which, by design, suffer from the paradox that a rational market should not allow for misvaluation. While the discrete time case has been extensively discussed in the literature and is most criticized for its failure to comply with rational expectations equilibria, we argue that this carries over to the finite time “strict local martingale”-approach to bubbles.

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CALCULATION, ADAPTATION AND RATIONAL EXPECTATIONS

Macroeconomic Dynamics ◽

10.1017/s1365100598007020 ◽

1998 ◽

Vol 2 (2) ◽

pp. 156-182 ◽

Cited By ~ 26

Author(s):

George W. Evans ◽

Garey Ramey

Keyword(s):

Adaptive Learning ◽

Rational Expectations ◽

Structural Changes ◽

Asset Price ◽

Learning Rule ◽

Calculation Algorithm ◽

Asset Price Bubbles ◽

Price Bubbles ◽

Rapid Adjustment ◽

Policy Shifts

We propose an active cognition approach to bounded rationality, in which agents use a calculation algorithm to improve on the forecasts provided by a purely adaptive learning rule such as least-squares learning. Agents' choices of calculation intensity depend on their estimates of the benefits of improved forecasts relative to calculation costs. Using an asset-pricing model, we show how more rapid adjustment to rational expectations and forward-looking behavior arise naturally when there are large anticipated structural changes such as policy shifts. We also give illustrative applications in which the severity of asset price bubbles and the intensity of hyperinflationary episodes are related to the cognitive ability of the agents.

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A Deterministic Description of Irrational and Semi-Rational Bubbles in Asset Markets

International Journal of Financial Management ◽

10.21863/ijfm/2015.5.2.012 ◽

2015 ◽

Vol 5 (2) ◽

Author(s):

Tanmoy Ganguli

Keyword(s):

Asset Price ◽

Time Frame ◽

Asset Markets ◽

Mathematical Representation ◽

Asset Price Bubbles ◽

Rational Bubbles ◽

Price Bubbles ◽

Hyman Minsky ◽

Linear Maps ◽

Deterministic Description

This present work provides a deterministic description irrational and semi-rational bubbles based on the stylized description forwarded by Hyman Minsky (1972), Day and Huang (1990) respectively. The paper emphasizes on two areas: First, it proposes a mathematical representation of an irrational bubble using piece-wise linear maps in a discrete time frame. Second, it studies the chaotic signals generated by them to explain the instability in asset price bubbles and explains the factors which impact their longevity.

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Monetary Policy and Bubbles in a New Keynesian Model with Overlapping Generations

American Economic Journal Macroeconomics ◽

10.1257/mac.20180427 ◽

2021 ◽

Vol 13 (2) ◽

pp. 121-167

Author(s):

Jordi Galí

Keyword(s):

Monetary Policy ◽

Rational Expectations ◽

Overlapping Generations ◽

Asset Price ◽

New Keynesian ◽

New Keynesian Model ◽

Asset Price Bubbles ◽

Price Bubbles ◽

Keynesian Model ◽

Welfare Implications

I analyze an extension of the New Keynesian model that features overlapping generations of finitely lived agents and (stochastic) transitions to inactivity. In contrast with the standard model, the proposed framework allows for the existence of rational expectations equilibria with asset price bubbles. I study the conditions under which bubble-driven fluctuations may emerge and the type of monetary policy rules that may prevent them. I conclude by discussing some of the model’s welfare implications. (JEL E12, E32, E44, E52, E63)

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BOLHAS RACIONAIS, CICLO DE PREÇOS DE ATIVOS E RACIONALIDADE LIMITADA: UMA AVALIAÇÃO CRÍTICA DOS MODELOS NEOCLÁSSICOS DE BOLHAS ESPECULATIVAS

Análise Econômica ◽

10.22456/2176-5456.10732 ◽

2009 ◽

Vol 21 (40) ◽

Author(s):

José Luís Oreiro

Keyword(s):

Bounded Rationality ◽

Rational Expectations ◽

Multiple Equilibria ◽

Asset Price ◽

Complete Information ◽

Unified Framework ◽

Asset Price Bubbles ◽

Price Bubbles ◽

Starting Point ◽

Asset Price Cycles

The objective of this article is to criticize neoclassical models of asset price bubbles and to argue that a general theory of asset price cycles demands the substitution of rational expectations hypothesis for bounded rationality assumption. In order to do that we will initially present the two neoclassical approaches for the problem of asset price bubbles. The first one, based on models of multiple equilibria with rational expectations, take financial markets as competitive and investors's behavior as based on perfect and complete information. In this setting, asset bubbles are a logically possible but unprobable phenomenon since their ocurrence will be associated with problems of dynamic ineficience which are not a relevant problem for most of capitalist economies. The second approach, initially developed by Krugman, take as a starting point the idea that financial market are far from perfect. In fact, these markets have a great number of imperfections as, for example, moral hazard. In this approach, asset price bubbles are the result of trading in assets with low supply-price elasticity as, for example, equities and land. Although this second approach is more realistic than the first, it is not capable to explain in a unified framework the appearance, propagation and burst of the speculative bubble; i.e the phenomenon of asset price cycles. This second approach is only capable to show the conditions for the existence of an asset bubble; but it is not capable to explain the dynamic evolution of the bubble. This question is better adressed by heterodox literature based on the hypothesis of bounded rationality.

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Asset price bubbles: Invariance theorems

Frontiers of Mathematical Finance ◽

10.3934/fmf.2021006 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Robert Jarrow ◽

Philip Protter ◽

Jaime San Martin

Keyword(s):

Asset Price ◽

Martingale Measure ◽

Local Martingale ◽

Statistical Probability ◽

Asset Price Bubbles ◽

Price Bubbles ◽

New Family ◽

Price Bubble ◽

Markov Diffusion ◽

Strict Local Martingale

<p style='text-indent:20px;'>This paper provides invariance theorems that facilitate testing for the existence of an asset price bubble in a market where the price evolves as a Markov diffusion process. The test involves only the properties of the price process' quadratic variation under the statistical probability. It does not require an estimate of either the equivalent local martingale measure or the asset's drift. To augment its use, a new family of stochastic volatility price processes is also provided where the processes' strict local martingale behavior can be characterized.</p>

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