Asset price bubbles: Invariance theorems

Robert Jarrow; Philip Protter; Jaime San Martin

doi:10.3934/fmf.2021006

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>

Download Full-text

INEFFICIENT BUBBLES AND EFFICIENT DRAWDOWNS IN FINANCIAL MARKETS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024920500478 ◽

2020 ◽

Vol 23 (07) ◽

pp. 2050047 ◽

Cited By ~ 1

Author(s):

MICHAEL SCHATZ ◽

DIDIER SORNETTE

Keyword(s):

Rational Expectations ◽

Rational Expectation ◽

Asset Price ◽

Theoretical Background ◽

Local Martingale ◽

Management Problem ◽

Market Failures ◽

Asset Price Bubbles ◽

Price Bubbles ◽

Hyman Minsky

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.

Download Full-text

TRANSACTION SERVICES AND ASSET-PRICE BUBBLES

Macroeconomic Dynamics ◽

10.1017/s1365100507070198 ◽

2008 ◽

Vol 12 (3) ◽

pp. 378-403

Author(s):

KEIICHIRO KOBAYASHI

Keyword(s):

Resource Allocation ◽

Steady State ◽

Asset Price ◽

Equilibrium Concept ◽

Asset Price Bubbles ◽

Price Bubbles ◽

Equilibrium Allocation ◽

Price Bubble ◽

Transaction Services ◽

Self Reference

This paper examines asset-price bubbles in an economy where a nondepletable asset (e.g., land) can provide transaction services, using a variant of the cash-in-advance model. When a landowner can borrow money immediately using land as collateral, one can say that land essentially provides a transaction service. The transaction services that such an asset can provide increase as its price rises, as the asset owner can borrow more money against the asset's increased value. Thus, an asset-price bubble can emerge due to the externality of self-reference, wherein the asset price reflects the transaction services that it can provide, whereas the amount of the transaction services reflects the asset price. If the collateral ratio of the asset (θ) and money supply (m) are not very large, a steady-state equilibrium exists where the asset price has a bubble component and resource allocation is inefficient; if θ and/or m become large, the bubble component of the asset price vanishes and the equilibrium allocation becomes efficient. The paper shows that in the case where the equilibrium concept is relaxed to allow for sticky prices and a temporary supply-demand gap, an equilibrium exists where a bubble develops temporarily and eventually bursts.

Download Full-text

Monetary Policy and Rational Asset Price Bubbles

The American Economic Review ◽

10.1257/aer.104.3.721 ◽

2014 ◽

Vol 104 (3) ◽

pp. 721-752 ◽

Cited By ~ 117

Author(s):

Jordi Galí

Keyword(s):

Monetary Policy ◽

Interest Rates ◽

Aggregate Demand ◽

Asset Price ◽

Optimal Monetary Policy ◽

Monetary Policies ◽

Asset Price Bubbles ◽

Price Bubbles ◽

Price Bubble ◽

The Impact

I examine the impact of alternative monetary policy rules on a rational asset price bubble, through the lens of an overlapping generations model with nominal rigidities. A systematic increase in interest rates in response to a growing bubble is shown to enhance the fluctuations in the latter, through its positive effect on bubble growth. The optimal monetary policy seeks to strike a balance between stabilization of the bubble and stabilization of aggregate demand. The paper's main findings call into question the theoretical foundations of the case for “leaning against the wind” monetary policies. (JEL E13, E32, E44, E52, G12)

Download Full-text

Are Real Estate Prices Evolving into an Asset Price Bubble?

ACTA VŠFS Ekonomicke studie a analyzy ◽

10.37355/acta-2021/1-02 ◽

2021 ◽

Vol 15 (1) ◽

pp. 36-48

Author(s):

Wolfgang Kloppenburg

Keyword(s):

Real Estate ◽

Interest Rates ◽

Asset Price ◽

Oecd Countries ◽

Real Estate Market ◽

Private Debt ◽

Asset Price Bubbles ◽

Price Bubbles ◽

Price Bubble ◽

Real Estate Prices

The development of real estate prices is of extraordinary importance for the fi nancial and economic system, as undesirable developments could endanger fi nancial stability – as seen in the fi nancial crisis of 2008 and 2009. This applies not only to speculators, but also to private households, which have to borrow to pay the purchase price. The market has been “fueled” in particular by the monetary policy of the central banks – expansion of the money supply and low interest rates. Investors are looking for investment opportunities due to the money glut, and the real estate market still promises a return. Furthermore, many people looking to build are willing to go into debt to buy a property. This demand ultimately has a driving eff ect on real estate prices. The aim of this paper is to compare and analyze the development of real estate prices in the most important OECD countries with those of Germany. A model of real estate prices is presented, which takes into account the most important indicators and provides information on when a price bubble exists. The model shows that asset price bubbles can be identified in some OECD countries. In Germany, on the other hand, there are only signs of a price bubble in a few major cities. Since private debt is low, it does not seem to be a problem across the board in Germany. A general problem remains with regard to the timely detectability of price bubbles.

Download Full-text

The Regional Pattern of the U.S. House Price Bubble – An Application of SPC to City Level Data

Review of Economics ◽

10.1515/roe-2015-0204 ◽

2015 ◽

Vol 66 (2) ◽

Cited By ~ 2

Author(s):

Julia Freese

Keyword(s):

Asset Price ◽

House Price ◽

Statistical Process ◽

Asset Price Bubbles ◽

Price Bubbles ◽

Ewma Control Chart ◽

Price Bubble ◽

Level Data ◽

Starting Point ◽

House Price Bubble

AbstractThe recent U.S. house price bubble and the subsequent deep financial crisis have renewed the interest in reliable identification methods for asset price bubbles. While there is a growing number of studies focussing on the detection of U.S. regional bubbles, estimations of the likely starting points in different local U.S. markets are still rare. Using regional data from 1990 to 2010 methods of Statistical Process Control (SPC) are used to test for house price bubbles in 17 major U.S. cities. Based on the EWMA control chart we also present estimations of the likely starting point of the regional bubbles. As a result, we find indications of house price bubbles in all 17 considered cities. Interestingly enough, the recent bubble was not a homogeneous event since regional starting points range from 1996 to 2002.

Download Full-text

FORWARD AND FUTURES PRICES WITH BUBBLES

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024909005518 ◽

2009 ◽

Vol 12 (07) ◽

pp. 901-924 ◽

Cited By ~ 16

Author(s):

ROBERT A. JARROW ◽

PHILIP PROTTER

Keyword(s):

Asset Price ◽

Option Prices ◽

Futures Prices ◽

Empirical Estimation ◽

Spot Prices ◽

Asset Price Bubbles ◽

Price Bubbles ◽

Canonical Process ◽

Put Option ◽

Price Bubble

This paper extends and refines the Jarrow et al. (2006, 2008) arbitrage free pricing theory for bubbles to characterize forward and futures prices. Some new insights are obtained in this regard. In particular, we: (i) provide a canonical process for asset price bubbles suitable for empirical estimation, (ii) discuss new methods to test empirically for asset price bubbles using both spot prices and call/put option prices on the spot commodity, (iii) show that futures prices can have bubbles independent of the underlying asset's price bubble, (iv) relate forward and futures prices under bubbles, and (v) relate price options on futures with asset price bubbles.

Download Full-text

FINANCIAL CRISIS IN THE DEVELOPING WORLD - POST THE US "ASSET PRICE BUBBLE DEBACLE" - A NEW WAY FORWARD

Buletin Ekonomi Moneter dan Perbankan ◽

10.21098/bemp.v12i1.465 ◽

2010 ◽

Vol 12 (1) ◽

pp. 5-26

Author(s):

Ms. Sagarika Chakraborty ◽

Mr. Soumya Banerjee

Keyword(s):

Monetary Policy ◽

Aggregate Demand ◽

Asset Price ◽

Capital Requirements ◽

Balance Sheets ◽

Asset Price Bubbles ◽

Price Bubbles ◽

Regulatory Policies ◽

Price Bubble ◽

Scientific Principles

This paper analyze how we should respond to possible asset price bubbles, especially in view of the various conceptual frameworks proposed based on a core set of scientific principles for monetary policy. Further, efforts have also been made at my end to establish as to how Monetary policy should not react to asset price bubbles per se, but rather to changes in the outlook for inflation and aggregate demand resulting from asset price movements. However, regulatory policies and supervisory practices should respond to possible asset price bubbles and help prevent feedback loops between asset price bubbles and credit provision, thereby minimizing the damaging effects of bubbles on the economy.The general massage of this paper is that credit conditions influence economies enormously and emergency steps to restructure balance sheets through policy revamping are crucial for fixing problems of excessive leverage. This stands in sharp contrast to the view from conventional models - that 'the effects of a worsening of financial intermediation are likely to be limited' and can be handled by interest rate cuts alone.In the alternative regulatory policy approach, we have strived to examine three possible regulatory responses to managing bubbles: portfolio restrictions; adjustments in capital requirements; and adjustments in provisioning requirements.JEL Classification: E58, E63, G15Keywords:financial crisis, asset price bubble.

Download Full-text