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Hurst exponents, Markov processes, and fractional Brownian motion

McCauley, Joseph L.; Gunaratne, Gemunu H.; Bassler, Kevin E. - In: Physica A: Statistical Mechanics and its Applications 379 (2007) 1, pp. 1-9

-infinite time interval is identical to that for a scaling Gaussian Markov process with H≠12 over a finite time interval. We conclude …

Persistent link: https://www.econbiz.de/10011062663

Martingales, nonstationary increments, and the efficient market hypothesis

McCauley, Joseph L.; Bassler, Kevin E.; Gunaratne, Gemunu H. - In: Physica A: Statistical Mechanics and its Applications 387 (2008) 15, pp. 3916-3920

We discuss the deep connection between nonstationary increments, martingales, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). We explain why a test for a martingale is generally a test for uncorrelated increments. We explain why...

Persistent link: https://www.econbiz.de/10010588900

Markov processes, Hurst exponents, and nonlinear diffusion equations: With application to finance

Bassler, Kevin E.; Gunaratne, Gemunu H.; McCauley, Joseph L. - In: Physica A: Statistical Mechanics and its Applications 369 (2006) 2, pp. 343-353

correlations like those found in fractional Brownian motion (fBm). We construct a large set of scaling solutions of Fokker … increments. For the scaling solutions, we show how to reduce the calculation of the probability density to a single integration … implies correlations fails for Markov processes with scaling solutions. Finally, we discuss the question of scaling of the …

Persistent link: https://www.econbiz.de/10011058407

Scaling, self-similarity and multifractality in FX markets

Xu, Zhaoxia; Gençay, Ramazan - In: Physica A: Statistical Mechanics and its Applications 323 (2003) C, pp. 578-590

This paper presents an empirical investigation of scaling and multifractal properties of US Dollar–Deutschemark (USD … exhibit power-law scaling in the tails. To test the multifractal properties of USD–DEM returns, the mean moment of the … different slopes for these powers of absolute returns. The nonlinearity of the scaling exponent indicates that the returns are …

Persistent link: https://www.econbiz.de/10010872935

Dynamics of real financial markets: A reply to Frank’s comment

Bassler, Kevin E.; Gunaratne, Gemunu H.; McCauley, Joseph L. - In: Physica A: Statistical Mechanics and its Applications 387 (2008) 13, pp. 3239-3241

This reply addresses the assertion in the comment of T.D. Frank [T.D. Frank, Physica A 387 (2008) 773] on our paper [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343] that the approach to modeling financial markets that we propose is unrealistic. In our paper, we considered...

Persistent link: https://www.econbiz.de/10011061331

Scaling and long-range dependence in option pricing III: A fractional version of the Merton model with transaction costs

Wang, Xiao-Tian; Yan, Hai-Gang; Tang, Ming-Ming; Zhu, En-Hui - In: Physica A: Statistical Mechanics and its Applications 389 (2010) 3, pp. 452-458

A model for option pricing of fractional version of the Merton model with ‘Hurst exponent’ H being in [1/2,1) is established with transaction costs. In particular, for H∈(1/2,1) the minimal price Cmin(t,St) of an option under transaction costs is obtained, which displays that the timestep...

Persistent link: https://www.econbiz.de/10011058111

Refined scaling hypothesis for anomalously diffusing processes

Badii, R.; Talkner, P. - In: Physica A: Statistical Mechanics and its Applications 291 (2001) 1, pp. 229-243

not scale like power laws, as generally assumed. A much improved scaling function is deduced, in analogy with a procedure … first applied to nearest-neighbour dimension estimators. Extremely accurate determination of the scaling exponents is thus …

Persistent link: https://www.econbiz.de/10010590063

Analysis of market efficiency for the Shanghai stock market over time

Wang, Yudong; Liu, Li; Gu, Rongbao; Cao, Jianjun; Wang, … - In: Physica A: Statistical Mechanics and its Applications 389 (2010) 8, pp. 1635-1642

In this paper, we analyze market efficiency for the Shanghai stock market over time using a model-free method known as multifractal detrended fluctuation analysis. Through analyzing the change of scale behavior, we find that the price-limited reform improved the efficiency in the long term, but...

Persistent link: https://www.econbiz.de/10010872297

Hurst exponents for interacting random walkers obeying nonlinear Fokker–Planck equations

Kumar, Niraj; Viswanathan, G.M.; Kenkre, V.M. - In: Physica A: Statistical Mechanics and its Applications 388 (2009) 18, pp. 3687-3694

Anomalous diffusion of random walks has been extensively studied for the case of non-interacting particles. Here we study the evolution of nonlinear partial differential equations by interpreting them as Fokker–Planck equations arising from interactions among random walkers. We extend the...

Persistent link: https://www.econbiz.de/10010874013

Characterizing bid–ask prices in the Brazilian equity market

Cajueiro, Daniel O.; Tabak, Benjamin M. - In: Physica A: Statistical Mechanics and its Applications 373 (2007) C, pp. 627-633

This paper presents evidence of long-range dependence in bid–ask prices for individual equity prices in the Brazilian stock market. Moreover, using the Hurst exponent calculated by the Local Whittle method as a measure of long-range dependence, we find evidence supporting that bid–ask prices...

Persistent link: https://www.econbiz.de/10010588591