Thomas Guhr

Publications (10)0 Total impact

• Article: Non-Stationarity in Financial Time Series and Generic Features

  Thilo A. Schmitt, Desislava Chetalova, Rudi Schäfer, Thomas Guhr
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  ABSTRACT: Financial markets are prominent examples for highly non-stationary systems. Sample averaged observables such as variances and correlation coefficients strongly depend on the time window in which they are evaluated. This implies severe limitations for approaches in the spirit of standard equilibrium statistical mechanics and thermodynamics. Nevertheless, we show that there are similar generic features which we uncover in the empirical return distributions for whole markets. We explain our findings by setting up a random matrix model.
  04/2013;
• Article: Microscopic understanding of heavy-tailed return distributions in an agent-based model

  Thilo A. Schmitt, Rudi Schäfer, Michael C. Münnix, Thomas Guhr
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  ABSTRACT: The distribution of returns in financial time series exhibits heavy tails. In empirical studies, it has been found that gaps between the orders in the order book lead to large price shifts and thereby to these heavy tails. We set up an agent based model to study this issue and, in particular, how the gaps in the order book emerge. The trading mechanism in our model is based on a double-auction order book, which is used on nearly all stock exchanges. In situations where the order book is densely occupied with limit orders we do not observe fat-tailed distributions. As soon as less liquidity is available, a gap structure forms which leads to return distributions with heavy tails. We show that return distributions with heavy tails are an order-book effect if the available liquidity is constrained. This is largely independent of the specific trading strategies.
  07/2012;
• Source

  Available from: Rudi Schäfer

  Article: Identifying States of a Financial Market

  Michael C. Münnix, Takashi Shimada, Rudi Schäfer, Francois Leyvraz Thomas H. Seligman, Thomas Guhr, H. E. Stanley
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  ABSTRACT: The understanding of complex systems has become a central issue because complex systems exist in a wide range of scientific disciplines. Time series are typical experimental results we have about complex systems. In the analysis of such time series, stationary situations have been extensively studied and correlations have been found to be a very powerful tool. Yet most natural processes are non-stationary. In particular, in times of crisis, accident or trouble, stationarity is lost. As examples we may think of financial markets, biological systems, reactors or the weather. In non-stationary situations analysis becomes very difficult and noise is a severe problem. Following a natural urge to search for order in the system, we endeavor to define states through which systems pass and in which they remain for short times. Success in this respect would allow to get a better understanding of the system and might even lead to methods for controlling the system in more efficient ways. We here concentrate on financial markets because of the easy access we have to good data and because of the strong non-stationary effects recently seen. We analyze the S&P 500 stocks in the 19-year period 1992-2010. Here, we propose such an above mentioned definition of state for a financial market and use it to identify points of drastic change in the correlation structure. These points are mapped to occurrences of financial crises. We find that a wide variety of characteristic correlation structure patterns exist in the observation time window, and that these characteristic correlation structure patterns can be classified into several typical "market states". Using this classification we recognize transitions between different market states. A similarity measure we develop thus affords means of understanding changes in states and of recognizing developments not previously seen.
  02/2012;
• Article: Identifying States of a financial market.

  Michael C Münnix, Takashi Shimada, Rudi Schäfer, Francois Leyvraz, Thomas H Seligman, Thomas Guhr, H Eugene Stanley
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  ABSTRACT: The understanding of complex systems has become a central issue because such systems exist in a wide range of scientific disciplines. We here focus on financial markets as an example of a complex system. In particular we analyze financial data from the S&P 500 stocks in the 19-year period 1992-2010. We propose a definition of state for a financial market and use it to identify points of drastic change in the correlation structure. These points are mapped to occurrences of financial crises. We find that a wide variety of characteristic correlation structure patterns exist in the observation time window, and that these characteristic correlation structure patterns can be classified into several typical "market states". Using this classification we recognize transitions between different market states. A similarity measure we develop thus affords means of understanding changes in states and of recognizing developments not previously seen.
  Scientific Reports 01/2012; 2:644.
• Source

  Available from: Rudi Schäfer

  Article: A Random Matrix Approach to Credit Risk

  Michael C. Münnix, Rudi Schäfer, Thomas Guhr
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  ABSTRACT: We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero. The existence of correlations alters the tails of the loss distribution considerably, even if their average is zero. Under the assumption of randomly fluctuating correlations, a lower bound for the estimation of the loss distribution is provided.
  02/2011;
• Source

  Available from: Rudi Schäfer

  Article: Statistical causes for the Epps effect in microstructure noise

  Michael C. Münnix, Rudi Schäfer, Thomas Guhr
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  ABSTRACT: We present two statistical causes for the distortion of correlations on high-frequency financial data. We demonstrate that the asynchrony of trades as well as the decimalization of stock prices has a large impact on the decline of the correlation coefficients towards smaller return intervals (Epps effect). These distortions depend on the properties of the time series and are of purely statistical origin. We are able to present parameter-free compensation methods, which we validate in a model setup. Furthermore, the compensation methods are applied to high-frequency empirical data from the NYSE's TAQ database. A major fraction of the Epps effect can be compensated. The contribution of the presented causes is particularly high for stocks that are traded at low prices. Comment: 8 pages, 7 figures
  09/2010;
• Source

  Available from: Rudi Schäfer

  Article: Impact of the tick-size on financial returns and correlations

  Michael C. Münnix, Rudi Schäfer, Thomas Guhr
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  ABSTRACT: We demonstrate that the lowest possible price change (tick-size) has a large impact on the structure of financial return distributions. It induces a microstructure as well as it can alter the tail behavior. On small return intervals, the tick-size can distort the calculation of correlations. This especially occurs on small return intervals and thus contributes to the decay of the correlation coefficient towards smaller return intervals (Epps effect). We study this behavior within a model and identify the effect in market data. Furthermore, we present a method to compensate this purely statistical error. Comment: 18 pages, 10 figures
  01/2010;
• Article: Power mapping with dynamical adjustment for improved portfolio optimization

  Rudi Schafer, Nils Fredrik Nilsson, Thomas Guhr
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  ABSTRACT: For financial risk management it is of vital interest to have good estimates for the correlations between the stocks. It has been found that the correlations obtained from historical data are covered by a considerable amount of noise, which leads to a substantial error in the estimation of the portfolio risk. A method to suppress this noise is power mapping. It raises the absolute value of each matrix element to a power q while preserving the sign. In this paper we use the Markowitz portfolio optimization as a criterion for the optimal value of q and find a K/T dependence, where K is the portfolio size and T the length of the time series. Both in numerical simulations and for real market data we find that power mapping leads to portfolios with considerably reduced risk. It compares well with another noise reduction method based on spectral filtering. A combination of both methods yields the best results.
  Quantitative Finance. 01/2010; 10(1):107-119.
• Source

  Available from: Rudi Schäfer

  Article: Compensating asynchrony effects in the calculation of financial correlations

  Michael C. Münnix, Rudi Schäfer, Thomas Guhr
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  ABSTRACT: We present a method to compensate statistical errors in the calculation of correlations on asynchronous time series. The method is based on the assumption of an underlying time series. We set up a model and apply it to financial data to examine the decrease of calculated correlations towards smaller return intervals (Epps effect). We show that this statistical effect is a major cause of the Epps effect. Hence, we are able to quantify and to compensate it using only trading prices and trading times. Comment: 13 pages, 7 figures
  10/2009;
• Source

  Available from: Rudi Schäfer

  Article: Credit risk - A structural model with jumps and correlations

  Rudi Schäfer, Markus Sjölin, Andreas Sundin, Michal Wolanski, Thomas Guhr
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  ABSTRACT: We set up a structural model to study credit risk for a portfolio containing several or many credit contracts. The model is based on a jump--diffusion process for the risk factors, i.e. for the company assets. We also include correlations between the companies. We discuss that models of this type have much in common with other problems in statistical physics and in the theory of complex systems. We study a simplified version of our model analytically. Furthermore, we perform extensive numerical simulations for the full model. The observables are the loss distribution of the credit portfolio, its moments and other quantities derived thereof. We compile detailed information about the parameter dependence of these observables. In the course of setting up and analyzing our model, we also give a review of credit risk modeling for a physics audience.
  08/2007;