105 citations · 310 across the 12 of their papers we have counts for
6 papers · 1 filter
Integration I(d) of Nonstationary Time Series: Stationary and nonstationary increments
Joseph L. McCauley, Kevin E. Bassler, Gemunu H. Gunaratne
The method of cointegration in regression analysis is based on an assumption of stationary increments. Stationary increments with fixed time lag are called integration I(d). A clas…
Martingales, Detrending Data, and the Efficient Market Hypothesis
Joseph L. McCauley, Kevin E. Bassler, Gemunu H. Gunaratne
We discuss martingales, detrending data, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independen…
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…
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…