Michael C. Münnix

• Ph.D.
• Boston University

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 ze...

Highly efficient single photon sources are of particular importance for quantum cryptography and quantum computation. Cavity-induced enhancement of spontaneous emission can improve photon generation efficiency in quantum-dot-based single photon sources dramatically. Using the eigenmode-technique, the authors calculate the 3-D distribution of the op...

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...

The efficient generation of polarized single or entangled photons is a crucial requirement for the implementation of quantum key distribution (QKD) systems. Self-organized semiconductor quantum dots (QDs) are capable of emitting one polarized photon or an entangled photon pair at a time using appropriate electrical current injection. We realized a...

Method and device for controlling a system state of a stationary system affected by delays as a function of a variable geoposition of a person, wherein the system is to have reached a predefined presence state when the person arrives at the location of the system. The method comprises: determining the geoposition of the person; estimating the time...

Supplementary Information

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 mecha...

Financial markets are becoming increasingly complex. The financial crisis of 2008 to 2009 has demonstrated that an improved understanding of the mechanisms embedded in the market is a key requirement for the estimation of financial risk. Recently, concepts of theoretical physics, in particular concepts of complex systems, have proven to be very use...

We analyze the statistical dependency structure of the S&P 500 constituents in the 4-year period from 2007 to 2010 using intraday data from the New York Stock Exchange's TAQ database. With a copula-based approach, we find that the statistical dependencies are very strong in the tails of the marginal distributions. This tail dependence is higher tha...

In financial context, the majority of studies in econophysics are dealing with market risk, since many concepts in statistical physics are directly applicable. A type of risk that is fundamentally different from the other types of financial risks discussed in the introduction is represented by credit risk [123–127]. Modeling credit risk, i.e., the...

The Epps effect describes the decrease of correlation estimates in financial data towards smaller return (or sampling-) intervals. This behavior has been of interest since Epps discovered this phenomenon in 1979 [89]. Since then, this behavior was found in data of different stock exchanges [90–93] and foreign exchange markets [94, 95]. An example f...

In this chapter, we pursue two different approaches to give insight into the statistical mechanics of a financial market.

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...

We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for similarity of previous market conditions to the present one. The resulting estimators are less biased and show lower variance than either unweighted or exponentially weighted estimato...

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...

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...

Efficient generation of polarized single photons or entangled photon pairs is a crucial requirement for the implementation of quantum key distribution (QKD) systems [1] [2]. In this context, self-organized semiconductor quantum dots (QDs) [3] [4] play a decisive role as they are capable of emitting only one polarized photon at a time using appropri...