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

Kevin E. Bassler, Gemunu H. Gunaratne and Joseph L. McCauley

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 13, 3239-3241

Abstract: 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 variable diffusion processes that have a diffusion coefficient that varies with both position (return in finance) and time, and used them to show that measuring a Hurst exponent H≠1/2 in a time series does not necessarily imply correlations between increments. We also proposed that such a variable diffusion process is the underlying stochastic process governing the dynamics of financial markets. Frank asserts that this is unrealistic because variable diffusion processes with H≠1/2 are driven with a “force” that varies in time as a power law. He claims, instead, that markets obey nonextensive thermostatistics. We discuss evidence from a recently published empirical study of the Euro–Dollar exchange rate [K.E. Bassler, J.L. McCauley, G.H. Gunaratne, PNAS 104 (2007) 17287] that shows that the market can be described with a variable diffusion process, but is inconsistent with nonextensive thermostatistics. This evidence demonstrates that our modeling approach is realistic and accurate.

Keywords: Variable diffusion; Stochastic processes; Markov processes; Hurst exponents; Time series analysis (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:13:p:3239-3241

DOI: 10.1016/j.physa.2008.02.009

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