Long correlations and Levy models applied to the study of memory effects in high frequency (tick) data

Mariani, Maria C.; Florescu, Ionuţ; Varela, M. P. Beccar; Ncheuguim, E.

doi:10.1016/j.physa.2008.12.038

Cited by 44 publications

(18 citation statements)

References 7 publications

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“…Alvarez-Ramirez et al (2008) applied DFA to evaluate the possibility of forecasting ability in oil prices, concluding that, in short periods of time, there was some persistence in the correlations, but for longer horizons (time spans greater than 25 days), such relationship ceased to exist. Analysing 26 different stocks of the NYSE on a given day, Mariani et al (2009) concluded that 19 out of 26 titles presented evidence of long memory, of which 18 had persistent behaviour and only one was anti-persistent. Muchnik et al (2009) did not use DFA to analyse returns or volatility directly, but rather to analyse the sequence of maxima and minima in the behaviour of various assets (stocks' prices and foreign exchange rates).…”

Section: Detrended Fluctuation Analysismentioning

confidence: 99%

Revisiting serial dependence in the stock markets of the G7 countries, Portugal, Spain and Greece

Ferreira

Dionísio

2014

Applied Financial Economics

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This article uses several tests to analyse serial dependence in financial data, trying to confirm the existence of some kind of nonlinear dependence in stock markets. In an attempt to provide a better explanation of the behaviour of stock markets, we used tests based on mutual information and detrended fluctuation analysis (DFA). Applying these tests to the series of stock market indexes of 10 countries, we concluded for the absence of linear autocorrelation. However, with other tests, we found nonlinear serial dependence that affects the rates of return. With DFA, we found out that most return rate series have long-range dependence, which appears to be more pronounced for Spain, Greece and Portugal. To confirm the inefficiency of those markets, based on our results, we should prove the existence of abnormal profits.

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Section: Detrended Fluctuation Analysismentioning

confidence: 99%

Revisiting serial dependence in the stock markets of the G7 countries, Portugal, Spain and Greece

Ferreira

Dionísio

2014

Applied Financial Economics

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“…First, by considering non-overlapping windows we can lose extreme price differences calculated using prices from the non-overlapping windows. Second, in a previous study (Mariani et al, 2009) the authors have shown that returns calculated from tick data exhibit long memory behavior. Thus, even by considering non-overlapping windows one cannot guarantee that the observations are independent.…”

Section: Sampling Method Rare Event Detectionmentioning

confidence: 92%

Rare Events Analysis for High-Frequency Equity Data

Bozdog¹,

Florescu²,

Khashanah³

et al. 2011

Wilmott

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In this work we present a methodology to detect rare events which are defined as large price movement relative to the volume traded. We analyze the behavior of equity after the detection of these rare events. We provide methods to calibrate trading rules based on the detection of these events and we exemplify for a particular trading rule. We apply the methodology to tick data for thousands of equities over a period of five days. In order to draw comprehensive conclusions we group the equities into classes and we calculate probabilities of price recovery after these rare events and for each class. The methodology that we have developed is based on non-parametric statistics and makes no assumption about the distribution of the random variables in the study. ______________________________________________________________________________________

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“…Any model where the volatility is random is called a stochastic volatility model. An alternative approach where the asset price is modeled using jump diffusion processes as well as Lévy processes has been considered in [3,12,13] (without considering the impact of transaction costs).…”

Section: Stochastic Volatility Model With Transaction Costsmentioning

confidence: 99%

Numerical Solutions for Option Pricing Models Including Transaction Costs and Stochastic Volatility

Mariani¹,

Sengupta²,

Bezdek³

2012

Acta Appl Math

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The option pricing problem when the asset is driven by a stochastic volatility process and in the presence of transaction costs leads to solving a nonlinear partial differential equation. The nonlinear term in the PDE reflects the presence of transaction costs. Under a particular market completion assumption we derive the nonlinear PDE whose solution may be used to find the price of options. In this paper under suitable conditions, we give an algorithmic scheme to obtain the solution of the problem by an iterative method and provide numerical solutions using the finite difference method.

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Long correlations and Levy models applied to the study of memory effects in high frequency (tick) data

Cited by 44 publications

References 7 publications

Revisiting serial dependence in the stock markets of the G7 countries, Portugal, Spain and Greece

Revisiting serial dependence in the stock markets of the G7 countries, Portugal, Spain and Greece

Rare Events Analysis for High-Frequency Equity Data

Numerical Solutions for Option Pricing Models Including Transaction Costs and Stochastic Volatility

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