Academics Research on Bubble Theory

• Financial power laws: Empirical evidence, models, and mechanism, Lux, T. (2006).Financial power laws: Empirical evidence, models, and mechanism(No. 2006-12). Economics Working Paper. Financial markets (share markets, foreign exchange markets and others) are all characterized by a number of universal power laws. The most prominent example is the ubiquitous finding of a robust, approximately cubic power law characterizing the distribution of large returns. A similarly robust feature is long-range dependence in volatility (i.e., hyperbolic decline of its autocorrelation function). The recent literature adds temporal scaling of trading volume and multi-scaling of higher moments of returns. Increasing awareness of these properties has recently spurred attempts at theoretical explanations of the emergence of these key characteristics form the market process. In principle, different types of dynamic processes could be responsible for these power-laws. Examples to be found in the economics literature include multiplicative stochastic processes as well as dynamic processes with multiple equilibria. Though both types of dynamics are characterized by intermittent behavior which occasionally generates large bursts of activity, they can be based on fundamentally different perceptions of the trading process. The present chapter reviews both the analytical background of the power laws emerging from the above data generating mechanism as well as pertinent models proposed in the economics literature.     
• A rational asset pricing model for premiums and discounts on closedend funds: Thebubble theory, Jarrow, R., & Protter, P. (2017). A rational asset pricing model for premiums and discounts on closedend funds: The bubble theory.Mathematical Finance. This paper provides a new explanation for closedend fund (CEF)discounts and premiums using the local martingale theory of asset pricebubbles. This is a rational asset pricing model that is shown to beconsistent with the existing empirical evidence on CEF discounts/premiums.Additional testable implications of the model are derived, which awaitsubsequent research for their resolution. This bubble theory also appliesequally well to understanding discounts and premiums on exchange tradedfunds. 
• Significance of log-periodic precursors to financial crashes, Sornette, D., & Johansen, A. (2001). Significance of log-periodic precursors to financial crashes.Quantitative Finance,1(4), 452-471. We clarify the status of log-periodicity associated with speculative bubbles preceding financial crashes. In particular, we address Feigenbaum's criticism ([A article="1469-7688/1/3/306"] Feigenbaum J A 2001Quantitative Finance1346-60 [/A]) and show how it can be refuted. Feigenbaum's main result is as follows: 'the hypothesis that the log-periodic 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 analyse 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 log-periodicity 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 risk-aversion within the general stochastic discount factor theory. We suggest guidelines for the use of log-periodicity and explain how to develop and interpret statistical tests of log-periodicity. 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 may result from an amplification mechanism that may make them more predictable. 
• Bubbles, human judgment, and expert opinion, Shiller, R. J. (2002). Bubbles, human judgment, and expert opinion.Financial Analysts Journal,58(3), 18-26. Research in psychology tells us how even the experts can get caught up in speculative bubbles. The widespread public disagreement about whether the stock market has been undergoing a speculative bubble since about 1995 reflects an underlying disagreement about how to view human judgment and intellect. The concept of a speculative bubble seems to require that some form of investor credulity or foolishness be at work. The disagreement is about whether we can in reality attribute such foibles to investorsnotably, whether it is plausible to attribute such weaknesses to professional investors, the experts, who were apparently no more detached from the alleged bubble than other investors.   Bubbles, crashes, and endogenous expectations in experimental spot asset markets, Smith, V. L., Suchanek, G. L., & Williams, A. W. (1988). Bubbles, crashes, and endogenous expectations in experimental spot asset markets.Econometrica: Journal of the Econometric Society, 1119-1151. Spot asset trading is studied in an environment in which all investors receive the same dividend from a known probability distribution at the end of each of T = 15 (or 30) trading periods. Fourteen of twenty-two experiments exhibit price bubbles followed by crashes relative to intrinsic dividend value. When traders are experienced this reduces, but does not eliminate, the probability of a bubble. The regression of changes in mean price on lagged excess bids (number of bids minus the number of offers in the previous period), P"t - P"t-1 = @a = @b(B"t"-"1 - O"t"-"1), supports the hypothesis that -@a = E(d), the one-period expected value of the dividend, and that @b > O, where excess bids is a surrogate measure of excess demand arising from homegrown capital gains (losses) expectations. Thus when (B"t"-"1 - O"t"_"1) goes to zero we have convergence to rational expectations in the sense of Fama (1970), that arbitrage becomes unprofitable. The observed bubble phenomenon can also be interpreted as a form of temporary myopia (Tirole, 1982) from which agents learn that capital gains expectations are only temporarily sustainable, ultimately inducing common expectations, or "priors" (Tirole, 1982). Four of twenty-six experiments, all using experienced subjects, yield outcomes that appear to the "chart's eye" to converge "early" to rational expectations, although even in these cases we get @b > O, and small price fluctuations of a few cents that invite "scalping."     
• A speculative bubble in commodity futures prices? Crosssectional evidence, Sanders, D. R., & Irwin, S. H. (2010). A speculative bubble in commodity futures prices? Crosssectional evidence.Agricultural Economics,41(1), 25-32. Recent accusations against speculators in general and longonly commodity index funds in particular include: increasing market volatility, distorting historical price relationships, and fueling a rapid increase and decrease in the level of commodity prices. Some researchers have argued that these market participantsthrough their impact on market pricesmay have inadvertently prevented the efficient distribution of food aid to deserving groups. Certainly, this resultif substantiatedwould counter the classical argument that speculators make prices more efficient and thus improve the economic efficiency of the food marketing system. Given the very important policy implications, it is crucial to develop a more thorough understanding of longonly index funds and their potential market impact. Here, we review the criticisms (and rebuttals) levied against (and for) commodity index funds in recent U.S. Congressional testimonies. Then, additional empirical evidence is added regarding crosssectional market returns and the relative levels of longonly index fund participation in 12 commodity futures markets. The empirical results provide scant evidence that longonly index funds impact returns across commodity futures markets.