|
Abstract
|
|---|
Stochastic models for stock prices built on fractional Brownian motion have been studied since long-range dependence was observed in financial time-series by Mandelbrot in 1960s. We propose an explanatory market microstructure model comprising many small investors who are inactive most of the time, and show that the effect of investor inertia can be approximated by a process with long range dependence and non-Gaussian returns distributions, driven by a fractional Brownian motion. A wavelet-based analysis of high frequency S&P 500 data shows the extent of long-range dependence, as measured by the Hurst exponent, began to fall in the late 1990s. We conjecture that this increased efficiency in the market during that period was due to increased activity facilitated by the explosion in internet trading. The mathematical contributions are a functional central limit theorem for stationary semi-Markov processes, and approximation results for stochastic integrals of continuous martingales with respect to fractional Brownian motion. |
|
|