2012-02-08 papers

on Market Microstructure

Issue of 2012‒02‒08
two papers chosen by
Thanos Verousis

On Hurst exponent estimation under heavy-tailed distributions By Jozef Barunik; Ladislav Kristoufek
A non-linear model of trading mechanism on a financial market By N. Vvedenskaya; Y. Suhov; V. Belitsky

On Hurst exponent estimation under heavy-tailed distributions

By:	Jozef Barunik; Ladislav Kristoufek
Abstract:	In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal detrended fluctuation analysis (MF-DFA), detrending moving average (DMA) and generalized Hurst exponent approach (GHE) estimate Hurst exponent on independent series with different heavy tails. For this purpose, we generate independent random series from stable distribution with stability exponent {\alpha} changing from 1.1 (heaviest tails) to 2 (Gaussian normal distribution) and we estimate the Hurst exponent using the different methods. R/S and GHE prove to be robust to heavy tails in the underlying process. GHE provides the lowest variance and bias in comparison to the other methods regardless the presence of heavy tails in data and sample size. Utilizing this result, we apply a novel approach of the intraday time-dependent Hurst exponent and we estimate the Hurst exponent on high frequency data for each trading day separately. We obtain Hurst exponents for S&P500 index for the period beginning with year 1983 and ending by November 2009 and we discuss the surprising result which uncovers how the market's behavior changed over this long period.
Date:	2012–01
URL:	http://d.repec.org/n?u=RePEc:arx:papers:1201.4786&r=mst

A non-linear model of trading mechanism on a financial market

By:	N. Vvedenskaya; Y. Suhov; V. Belitsky
Abstract:	We introduce a prototype model in an attempt to capture some aspects of market dynamics simulating a trading mechanism. The model description starts with a discrete-space, continuous-time Markov process describing arrival and movement of orders with different prices. We then perform a re-scaling procedure leading to a deterministic dynamical system controlled by non-linear ordinary differential equations (ODEs). This allows us to introduce approximations for the equilibrium distribution of the model represented by fixed points of deterministic dynamics.
Date:	2012–01
URL:	http://d.repec.org/n?u=RePEc:arx:papers:1201.4580&r=mst

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