Bubble Beliefs
Christian Stolborg (Copenhagen Bus. School) and Robin Greenwood (Harvard)
October 2025
We study expert beliefs during boom-bust episodes in which highly valued individual US stocks experience a price run-up followed by a crash. As prices surge, analysts forecast exceptional earnings growth and high near-term returns. Short interest stays low. Media coverage rarely mentions the word “bubble”, even as crashes unfold. Optimism portends crashes: the most bullish forecasts predict the highest crash risk. The results are consistent with accounts of bubbles driven by overly optimistic expectations about fundamentals and future prices, with only limited presence of skeptics who recognize the bubble, apart from a few cases where the share lending market offers signals.
P-Bubbles, Q-Bubbles, and Risk Premia
Robert A. Jarrow (Cornell University) and Simon Kwok (University of Sydney)
August 2025
We develop a modeling framework that connects two distinct types of bubbles de ned in the literature: the rational bubbles (aka P-bubbles), and the local martingale bubbles (aka Q-bubbles). We relate both types of bubbles to an equity s risk premium via a novel decomposition. We empirically study this decomposition using a sample of stocks and ETFs, and nd that both types of bubbles are economically signi cant and important in understanding equity risk premium.
The Speculative Tech Bubbles of US Artificial Intelligence Sector
Aktham Issa Maghyereh (United Arab Emirates U.) and B. Awartani (King Fahd U.)
January 2025
In this study we identify synchronized multiple bubble episodes in leading US artificial intelligence companies during the pandemic market exuberance from 2020 to 2022, and then after the excessive optimism prevailed post 2023. Interestingly, the bubbles are found to be driven by liquidity, financial market stress and economic uncertainty. The investors’ sentiment is also found to influence the bubble formation. The results of this letter highlight the importance of fundamentally assessing the longer-term prospects of artificial intelligence companies.
The Bubble-Crash GARCH model
Andrea Montanino and Giovanni De Luca (University of Naples)
September 2025
Bubbles and flash crashes are tail events that threaten not only the stability of the financial system but also the effectiveness of investment, hedging, and diversification strategies. These phenomena have a significant impact on the conditional mean of asset returns and often serve as early signals of heightened market uncertainty. In recent years, several methodologies have been proposed to detect the emergence and collapse of such events. Among them, the Phillips, Shi, and Yu (PSY) test-based on the rational bubble model-has gained broad empirical acceptance among central banks and market practitioners for its effectiveness in identifying explosive price behavior. This study employs the Backward Supremum Augmented Dickey-Fuller (BSADF) version of the PSY test to locate and date-stamp rational bubbles and flash crashes in the cryptocurrency market. After identifying the presence and duration of these extreme events, two dummy variables are introduced as exogenous regressors in the mean equation of a GARCH framework. In this setting, the conditional mean does not follow a typical ARIMA process; rather, it is directly modeled as a function of the bubble and crash dummies, thereby capturing the structural impact of these events on expected returns. This extended specification-referred to as the Bubble Crash-GARCH (BC-GARCH) model-is evaluated against the standard GARCH framework to assess potential gains in volatility forecasting. Empirical evidence, based on the Diebold-Mariano test, confirms that the Bubble-Crash GARCH delivers statistically significant improvements in forecasting accuracy by enhancing the residuals of the mean equation. Furthermore, the model is augmented with two additional dummy variables capturing bubbles and crashes in Bitcoin, which, as will be shown, improve volatility forecasts for Bitcoin itself but also for other major cryptocurrencies, exerting a significant influence on their mean returns. By explicitly modeling bubbles and crashes alongside volatility, the overall degree of latent uncertainty is reduced, since these extreme events are disentangled and accounted for separately. This systematic treatment enhances the explanatory power of volatility models and provides meaningful insights for financial institutions and investors concerned with risk management and asset allocation.
Bubbles and Beyond: The Macroeconomic Drivers of Precious Metal Surges
Arusha V. Cooray (James Cook U.) and İbrahim Özmen (Selcuk U.)
November 2025
This study examines the movement in prices of precious metals, gold, silver, and platinum, and local inflation and interest rates, across a selection of resource rich countries, namely, the U.S, Germany, Italy, France, Switzerland and the Netherlands over the 2008 to 2023 period. The study focuses on identifying explosive bubble dynamics, persistent long memory patterns, and the role of structural breaks. Results show that price bubbles correspond to global financial crises, monetary expansions, and geopolitical tensions, reflecting investor reactions to uncertainty. Structural breaks align with regime shifts in monetary policy and political events, while long-memory characteristics highlight persistent risk perceptions, particularly for gold in the US and Switzerland. Cointegration analyses reveal heterogeneous relationships between precious metals and macroeconomic variables across countries. The findings advance understanding of precious metals as both speculative instruments and hedges against macroeconomic and geopolitical risks.
Bubble-Crash MSGARCH vs. MSGARCH: Forecasting Volatility and Backtesting Expected Shortfall in Bitcoin
Giovanni De Luca and Andrea Montanino (U. of Naples)
October 2025
Cryptocurrencies represent one of the most significant financial innovations of the twenty-first century. Their market has expanded rapidly, alongside growing integration into both institutional and retail investors’ portfolios. Economic authorities and central banks have often warned investors about their high levels of volatility relative to traditional assets. Over the past decade, several episodes of financial bubbles and also price crashes have characterized the dynamics of this market. This paper contributes to the literature extending the Markov-Switching GARCH (MSGARCH) framework by explicitly accounting for bubble and flash crash dynamics in Bitcoin. In fact, after testing for the presence of periodically collapsing bubbles and flash crashes in Bitcoin price using the PSY test, it incorporates the identified episodes into the MSGARCH specification to improve the modeling of regime-dependent volatility. The resulting model is termed the Bubble-Crash MSGARCH (BC-MSGARCH), that is the variant of the BC-GARCH model applied to the MS-GARCH framework. The introduction of the Bubble-Crash filter substantially improves model specification, capturing nonlinear dynamics that a simple ARMA-based filter fails to represent. In addition, empirical evidence for Bitcoin shows that incorporating bubble and crash phases into the mean equation of an MSGARCH model significantly enhances volatility forecasting performance. Moreover, the model can also achieve better results in the backtesting of the Expected Shortfall.
Learn To Use R For Portfolio Analysis
Quantitative Investment Portfolio Analytics In R:
An Introduction To R For Modeling Portfolio Risk and Return
By James Picerno
