Related papers: An Economic Bubble Model and Its First Passage Tim…
We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a…
In this paper we further extend the optimal bubble riding model proposed by Tangpi and Wang by allowing for price-dependent entry times. Agents are characterized by their individual entry threshold that represents their belief in the…
A new framework for asset pricing based on modelling the information available to market participants is presented. Each asset is characterised by the cash flows it generates. Each cash flow is expressed as a function of one or more…
Prices in financial markets exhibit extreme jumps far more often than can be accounted for by external news. Further, magnitudes of price changes are correlated over long times. These so called stylized facts are quantified by scaling laws…
This article provides a self-contained overview of the theory of rational asset price bubbles. We cover topics from basic definitions, properties, and classical results to frontier research, with an emphasis on bubbles attached to real…
What is the role of social interactions in the creation of price bubbles? Answering this question requires obtaining collective behavioural traces generated by the activity of a large number of actors. Digital currencies offer a unique…
Oil price data have a complicated multi-scale structure that may vary with time. We use time-frequency analysis to identify the main features of these variations and, in particular, the regime shifts. The analysis is based on a…
The aim of this paper is to compare statistical properties of a bubble period with those of the anti-bubble period in stock markets. We investigate the statistical properties of daily data for the Nikkei 225 index in the 28-year period from…
The drift burst hypothesis postulates the existence of short-lived locally explosive trends in the price paths of financial assets. The recent U.S. equity and treasury flash crashes can be viewed as two high-profile manifestations of such…
Asset price bubbles are situations where asset prices exceed the fundamental values defined by the present value of dividends. This paper presents a conceptually new perspective: the necessity of bubbles. We establish the Bubble Necessity…
We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self…
A new concept, called balanced estimator of diffusion entropy, is proposed to detect scalings in short time series. The effectiveness of the method is verified by means of a large number of artificial fractional Brownian motions. It is used…
We study a financial market where the risky asset is modelled by a geometric It\^o-L\'{e}vy process, with a singular drift term. This can for example model a situation where the asset price is partially controlled by a company which…
A dynamical model is introduced for the formation of a bullish or bearish trends driving an asset price in a given market. Initially, each agent decides to buy or sell according to its personal opinion, which results from the combination of…
Stock price changes occur through transactions, just as diffusion in physical systems occurs through molecular collisions. We systematically explore this analogy and quantify the relation between trading activity - measured by the number of…
We present a simple agent-based model to study the development of a bubble and the consequential crash and investigate how their proximate triggering factor might relate to their fundamental mechanism, and vice versa. Our agents invest…
Financial markets provide an ideal frame for the study of crossing or first-passage time events of non-Gaussian correlated dynamics mainly because large data sets are available. Tick-by-tick data of six futures markets are herein considered…
We develop a stochastic macro-financial model in continuous time by integrating two specifications of the Keen economic framework with a financial market driven by a jump-diffusion process. The economic block of the model combines monetary…
We present a heuristic argument for the propensity of Topological Data Analysis (TDA) to detect early warning signals of critical transitions in financial time series. Our argument is based on the Log-Periodic Power Law Singularity (LPPLS)…
We study the first-passage time (FPT) problem for widespread recurrent processes in confined though large systems and present a comprehensive framework for characterizing the FPT distribution over many time scales. We find that the FPT…