Fractional calculus and continuous-time finance II: the waiting-time distribution

By Francesco Mainardi, Marco Raberto, Rudolf Gorenflo, E. Bologna, University of Genoa, Free University of Berlin, University of Eastern Piedmont. 2000

508 citations recorded by the source corpus.

We complement the theory of tick-by-tick dynamics of financial markets based on a Continuous-Time Random Walk (CTRW) model recently proposed by Scalas et al., and we point out its consistency with the behaviour observed in the waiting-time distribution for BUND future prices traded at LIFFE, London.

Subfields: Economics and Econometrics, Finance, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3707e1aff2c0195f4fa0d6fe803baf78fde518bb

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Citations in the corpus

Detailed Error Analysis for a Fractional Adams Method (2004, unknown): “[17,27,41] (connections to the theory of random walks, the latter two papers especially with respect to applications to mathematical models in finance), Metzler et al.”
Logistic map with memory from economic model (2017, background): “We should note that the fractional calculus and fractional differential equations have a wide application to describe different economic and financial processes with memory and nonlocality [56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 15, 16, 17, 18, 19] in the continuous time approach.”
TEMPERED FRACTIONAL CALCULUS (2015, background): “They are now used to model a wide variety of problems in physics [24, 35,38,50,51,55,65], finance [23,27,37,42,60,61], biology [2,4,22,26,36], and hydrology [1,7,8,15,17,62].”
A second-order accurate numerical method for the two-dimensional fractional diffusion equation (2007, methodology): “Fractional diffusion equations are used to model problems in physics (see a comprehensive review by Metzler and Klafter [25]), finance [10,16,28,31,30], and hydrology [2,4,5,32,33].”
The application of continuous-time random walks in finance and economics (2006, methodology): “[1,37,55]) can be used to derive the following integral equation that gives the probability density, pðx; tÞ, for the particle of being in position x at time t, conditioned by the fact that it was in position x 1⁄4 0 at time t 1⁄4 0:”
Continuous-time random walk and parametric subordination in fractional diffusion (2007, unknown): “To this purpose we lay open our general view of subordination in stochastic processes in Section 4.”
Fractional vector calculus for fractional advection–dispersion (2006, background): “Fractional derivatives have recently been applied to many problems in physics [5–18], finance [15,19–22], and hydrology [23–28].”