The Martingale Theory of Bubbles: Implications for the Valuation of Derivatives and Detecting Bubbles

Robert A Jarrow and Philip Protter


Introduction to 'Lessons from the Financial Crisis'


The Credit Crunch of 2007: What Went Wrong? Why? What Lessons Can be Learned?


Underwriting versus Economy: A New Approach to Decomposing Mortgage Losses


The Shadow Banking System and Hyman Minsky’s Economic Journey


The Collapse of the Icelandic Banking System


The Quant Crunch Experience and the Future of Quantitative Investing


No Margin for Error: The Impact of the Credit Crisis on Derivatives Markets


The Re-Emergence of Distressed Exchanges in Corporate Restructurings


Modelling Systemic and Sovereign Risks


Measuring and Managing Risk in Innovative Financial Instruments


Forecasting Extreme Risk of Equity Portfolios with Fundamental Factors


Limits of Implied Credit Correlation Metrics Before and During the Crisis


Another view on the pricing of MBSs, CMOs and CDOs of ABS


Pricing of Credit Derivatives with and without Counterparty and Collateral Adjustments


A Practical Guide to Monte Carlo CVA


The Endogenous Dynamics of Markets: Price Impact, Feedback Loops and Instabilities


Market Panics: Correlation Dynamics, Dispersion and Tails


Financial Complexity and Systemic Stability in Trading Markets


The Martingale Theory of Bubbles: Implications for the Valuation of Derivatives and Detecting Bubbles


Managing through a Crisis: Practical Insights and Lessons Learned for Quantitatively Managed Equity Portfolios


Active Risk Management: A Credit Investor’s Perspective


Investment Strategy Returns: Volatility, Asymmetry, Fat Tails and the Nature of Alpha

After the 2007–9 credit crisis, caused by a crash in housing prices (the bursting of an alleged housing price bubble), asset price bubbles received considerable attention in the financial press and regulatory arena.11 See William Dudley, “Asset Bubbles and the Implications for Central Bank Policy”, speech, April 7, 2010 (available at Before this episode, however, the modelling of asset price bubbles had a long history in economics.

Classical economics studied the existence and characterisation of bubbles in discrete-time, infinite- and finite-horizon, equilibrium models. It has been shown that bubbles cannot exist in finite-horizon rational expectation models (Santos and Woodford 1997; Tirole 1982). They can arise, however, in markets where traders behave myopically (Tirole 1982), where there are irrational traders (De Long et al 1990), in infinite-horizon growing economies with rational traders (O’Connell and Zeldes 1988; Tirole 1985; Weil 1990), economies where rational traders have differential beliefs and when arbitrageurs cannot synchronise trades (Abreu and Brunnermeier 2003) or when there are short-sale/borrowing constraints (Santos and Woodford

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