The endo–exo problem in high frequency financial price fluctuations and rejecting criticality

Wheatley, Spencer; Wehrli, Alexander; Sornette, Didier

doi:10.1080/14697688.2018.1550266

Cited by 34 publications

(42 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It has been and continues to be a very useful model in geophysical, social, and financial systems. 1with an exponential kernel (13). The event occurring at a given time stamp is represented by a jump in the intensityν(t ), the probability per unit time that a next event will occur.…”

Section: B Definition Of the Hawkes Conditional Poisson Processmentioning

confidence: 99%

“…As the first example, we focus on the single exponential kernel (13). While this special case is analytically tractable without the need to refer to the master equation approach [52], we nevertheless derive its exact solution via the master equation approach, because the methodology will be readily generalized to the more complex cases.…”

Section: B Single Exponential Kernelmentioning

confidence: 99%

“…Here, we provide two different derivations of the power law PDF (53) of Hawkes intensities for the exponential memory kernel (13).…”

Section: Appendix A: Explicit Derivation Of the Master Equationsmentioning

confidence: 99%

“…[10] for a short review), as it was realized that some of the stochastic processes in financial markets can be well represented by this class of models [11], for which the triggering and branching processes capture the herding nature of market participants (be they due to psychological or rational imitation of human traders or as a result of machine learning and adapting). In field of financial economics, the Hawkes process has been successfully involved in issues as diverse as estimating the volatility at the level of transaction data, estimating the market stability [11][12][13], accounting for systemic risk contagion, devising optimal execution strategies, and capturing the dynamics of the full order book [14]. Another domain of intense use of the Hawkes model and its many variations is found in the field of social dynamics on the internet, including instant messaging and blogging such on Twitter [15] as well as the dynamics of book sales [16], video views [17], success of movies [18], and so on.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Field master equation theory of the self-excited Hawkes process

Kanazawa

Sornette

2020

Phys. Rev. Research

Self Cite

View full text Add to dashboard Cite

A field theoretical framework is developed for the Hawkes self-excited point process with arbitrary memory kernels by embedding the original non-Markovian one-dimensional dynamics onto a Markovian infinitedimensional one. The corresponding Langevin dynamics of the field variables is given by stochastic partial differential equations that are Markovian. This is in contrast to the Hawkes process, which is non-Markovian (in general) by construction as a result of its (long) memory kernel. We derive the exact solutions of the Lagrange-Charpit equations for the hyperbolic master equations in the Laplace representation in the steady state, close to the critical point of the Hawkes process. The critical condition of the original Hawkes process is found to correspond to a transcritical bifurcation in the Lagrange-Charpit equations. We predict a power law scaling of the probability density function (PDF) of the intensities in an intermediate asymptotic regime, which crosses over to an asymptotic exponential function beyond a characteristic intensity that diverges as the critical condition is approached. We also discuss the formal relationship between quantum field theories and our formulation. Our field theoretical framework provides a way to tackle complex generalization of the Hawkes process, such as nonlinear Hawkes processes previously proposed to describe the multifractal properties of earthquake seismicity and of financial volatility.

show abstract

Section: B Definition Of the Hawkes Conditional Poisson Processmentioning

confidence: 99%

Section: B Single Exponential Kernelmentioning

confidence: 99%

“…Here, we provide two different derivations of the power law PDF (53) of Hawkes intensities for the exponential memory kernel (13).…”

Section: Appendix A: Explicit Derivation Of the Master Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Field master equation theory of the self-excited Hawkes process

Kanazawa

Sornette

2020

Phys. Rev. Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…of financial markets [75][76][77]. As the "branching ratio" approaches 1, the market becomes more and more endogenous and the response time to shocks diverges, so that news have a longer and longer lived impact.…”

Section: Application To Rebsmentioning

confidence: 99%

Rational Belief Bubbles

Sohn

Sornette

2020

Front. Phys.

Self Cite

View full text Add to dashboard Cite

We propose an extension of the class of rational expectations bubbles (REBs) to the more general rational beliefs setting of [1, 2]. In a potentially non-stationary but stationarizable environment, among a heterogenous population of agents, it is possible to hold more than one "rational" expectation. When rational but diverse beliefs converge ("correlated beliefs"), they do not cancel each other out in aggregate anymore. This can make them an object of rational speculation. Accounting for the fact that market efficiency has an intrinsic time-dimension, we show that diverse but correlated beliefs can thus account for speculative bubbles, without the need for irrational agents or limits to arbitrage. Many of the shortcomings of REBs that make rational bubbles implausible can be overcome once we relax the ergodicity requirement. In particular, we argue that the hitherto unexplained "bubble component" of REBs corresponds to the extension of the state space in [3].

show abstract

Expectations of Linear and Nonlinear Hawkes Processes Using a Field-Theoretical Approach

Cui,

Sornette

2024

JABES

View full text Add to dashboard Cite

The endo–exo problem in high frequency financial price fluctuations and rejecting criticality

Cited by 34 publications

References 59 publications

Field master equation theory of the self-excited Hawkes process

Field master equation theory of the self-excited Hawkes process

Rational Belief Bubbles

Expectations of Linear and Nonlinear Hawkes Processes Using a Field-Theoretical Approach

Contact Info

Product

Resources

About