105 citations
4 papers
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…
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…
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…