105 citations · 529 across the 26 of their papers we have counts for
6 papers · 1 filter
Nonstationary Increments, Scaling Distributions, and Variable Diffusion Processes in Financial Markets
Kevin E. Bassler, Joseph L. McCauley, Gemunu H. Gunaratne
Arguably the most important problem in quantitative finance is to understand the nature of stochastic processes that underlie market dynamics. One aspect of the solution to this pr…
Hurst Exponents, Markov Processes, and Fractional Brownian motion
Joseph L. McCauley, Gemunu H. Gunaratne, Kevin E. Bassler
There is much confusion in the literature over Hurst exponents. Recently, we took a step in the direction of eliminating some of the confusion. One purpose of this paper is to illu…
Linear vs. Nonlinear Diffusion and Martingale Option Pricing
J. L. McCauley, G. H. Gunaratne, K. E. Bassler
First, classes of Markov processes that scale exactly with a Hurst exponent H are derived in closed form. A special case of one class is the Tsallis density, advertised elsewhere a…
Martingale Option Pricing
J. L. McCauley, G. H. Gunaratne, K. E. Bassler
We show that our generalization of the Black-Scholes partial differential equation (pde) for nontrivial diffusion coefficients is equivalent to a Martingale in the risk neutral dis…
Response to Worrying Trends in Econophysics
Joseph L. McCauley
This article is a response to the recent Worrying Trends in Econophysics critique written by four respected theoretical economists. Two of the four have written books and papers th…
Markov Processes, Hurst Exponents, and Nonlinear Diffusion Equations with application to finance
Kevin E. Bassler, Gemunu H. Gunaratne, Joseph L. McCauley
We show by explicit closed form calculations that a Hurst exponent H that is not 1/2 does not necessarily imply long time correlations like those found in fractional Brownian motio…