The continuous time random walk formalism in financial markets

Masoliver, Jaume; Montero, Miquel; Perelló, Josep; Weiss, George H.

doi:10.1016/j.jebo.2004.07.015

Cited by 67 publications

(81 citation statements)

References 23 publications

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“…In particular the crossover between more and less anomalous behavior has been observed in the volatility of some share prices [28]. Here, we compare the numerical results of the finite difference schemes (13), (14) with those of the numerical scheme in [20].…”

Section: Respectivelymentioning

confidence: 97%

High‐order compact difference schemes for the modified anomalous subdiffusion equation

Ding

2015

Numerical Methods Partial

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In this paper, two kinds of high-order compact finite difference schemes for second-order derivative are developed. Then a second-order numerical scheme for a Riemann-Liouvile derivative is established based on a fractional centered difference operator. We apply these methods to a fractional anomalous subdiffusion equation to construct two kinds of novel numerical schemes. The solvability, stability and convergence analysis of these difference schemes are studied by using Fourier method. The convergence orders of these numerical schemes are O(τ 2 + h 6 ) and O(τ 2 + h 8 ), respectively. Finally, numerical experiments are displayed which are in line with the theoretical analysis.

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Section: Respectivelymentioning

confidence: 97%

High‐order compact difference schemes for the modified anomalous subdiffusion equation

Ding

2015

Numerical Methods Partial

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“…Let us begin with a short review of the theory of CTRWs; for a more detailed explanation see, e.g., [25]. The CTRW X a (t) is a stochastic process that, at random instants of time, 0 = t 0 t 1 · · · t n−1 t n , suffers random changes or jumps of magnitude J n ,…”

Section: Ctrws Without Memorymentioning

confidence: 99%

Parrondo-like behavior in continuous-time random walks with memory

Montero

2011

Phys. Rev. E

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The continuous-time random walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this paper we will show how the random combination of two different unbiased CTRWs can give rise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought of as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same as that of the Parrondo paradox in game theory.

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“…Recently, its application to description of financial time-series was proposed [3][4][5][6][7][8][9][10][11][12]. In the traditional CTRW, times duration and jumps are independent random variables and in the most of cases their distribution are static.…”

Section: Introductionmentioning

confidence: 99%