Narrow Results

This study aims to exploit the Artificial intelligence (AI)-based computing paradigm to analyze the economic system to define the price movements of unsustainable expansion, rapid collapse, and eventual equilibrium that characterize financial bubbles represented with differential equations to portray the role of societal contagion and group mentality from a behavioral viewpoint with the market population classified as bull, i.e., optimistic, neutrals, bear, i.e., pessimistic, and quitter categories. The concept of the financial bubble is characterized as an unexpected rise in prices that is rapidly followed by a shrill decline and retrospectively appears as a consequence of such uncertainty in price value. AI-based applications facilitate financial analysts with innovative computational paradigms for gaining deep insights, improving predictive accuracy, and creating sustained vigorous risk management stratagems for the financial bubble framework and solving with supervised nonlinear autoregressive exogenous networks with optimized Bayesian regularization algorithm to accomplish the reasonable predictive accuracy and malleability for the solution of financial bubble behavioral dynamics. The Adams numerical solver accomplishes the acquisition of synthetic data for the execution of a multi-layer structure of exogenous networks to solve for financial bubble parameters termed as contagion rate of optimistic behavior, bearish behavior, pessimist’s average time of staying in the bearish group, the pessimist’s population effect on the autonomous supply and the rate of optimists conversion to pessimists group while assuming other parameters values to be fixed for demand and supply functions. A consistent overlap between proposed results and synthetic numerical values of a financial bubble model is indicated by negligible error value that verifies the exogenous network’s effectiveness and is verified by the enclosure of several evaluation measures of the precision and efficiency, through mean square error objective functions, adaptive amendable parameters, error dispersal, and input-error correlation analyses.

Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA) are signal numerical analysis methodologies able to work with nonlinear dynamical systems and nonstationarity. Moreover, they well evidence changes in the states of a dynamical system. We recall their features and give practical recipes. It is shown that RP and RQA detect the critical regime in financial indices (in analogy with phase transition) before a bubble bursts, whence allowing to estimate the bubble initial time. The analysis is made on DAX and NASDAQ daily closing price between January 1998 and November 2003. DAX is studied in order to set-up overall considerations, and as a support for deducing technical rules. The NASDAQ bubble initial time has been estimated to be on 19 October 1999.

In a numéraire-independent framework, we study a financial market with $N$ assets which are all treated in a symmetric way. We define the fundamental value ^∗S of an asset $S$ as its super-replication price and say that the market has a strong bubble if ^∗S and $S$ deviate from each other. None of these concepts needs any mention of martingales. Our main result then shows that under a weak absence-of-arbitrage assumption (basically NUPBR), a market has a strong bubble if and only if in all numéraire s for which there is an equivalent local martingale measure (ELMM), asset prices are strict local martingales under all possible ELMMs. We show by an example that our bubble concept lies strictly between the existing notions from the literature. We also give an example where asset prices are strict local martingales under one ELMM, but true martingales under another, and we show how our approach can lead naturally to endogenous bubble birth.

We present a methodology to identify change-points in financial markets where the governing regime shifts from a constant rate-of-return, i.e. normal growth, to a superexponential growth described by a power-law hazard rate. The latter regime corresponds, in our view, to financial bubbles driven by herding behavior of market participants. Assuming that the time series of log-price returns of a financial index can be modeled by arithmetic Brownian motion, with an additional jump process with power-law hazard function to approximate the superexponential growth, we derive a threshold value of the hazard-function control parameter, allowing us to decide in which regime the market is more likely to be at any given time. An analysis of the Standard & Poors 500 index over the last 60 years provides evidence that the methodology has merit in identifying when a period of herding behavior begins, and, perhaps more importantly, when it ends.

To assist with the detection of bubbles and negative bubbles in financial markets, a criterion is introduced to indicate whether a market is likely to be in a superexponential regime (where growth in such a regime would correspond to an asset price bubble and decline to an negative bubble) as opposed to “normal” exponential behavior typified by a constant rate of growth or decline. The criterion is founded on the Johansen–Ledoit–Sornette model of asset dynamics in a bubble and is derived from a linear fit to observed data with a nonlinear time transformation with parameters distributed uniformly in their permitted ranges. Making use of expected values rather than the underlying distribution, the criterion is straightforward and efficient to compute and can in principle be applied in real time to intra-day markets as well as longer timescales. In some circumstances, the criterion is shown to have certain predictive qualities when applied to a portfolio of stocks, and could be used as input into algorithmic trading strategies. A simple strategy is described which is based on market reversion predictions of a portfolio of stocks and which in back-testing generates notable returns.