Statistical Finance
We present a theory of homogeneous volatility bridge estimators for log-price stochastic processes. The main tool of our theory is the parsimonious encoding of the information contained in the open, high and low prices of incomplete bridge,…
In our previous studies we have investigated the structural complexity of time series describing stock returns on New York's and Warsaw's stock exchanges, by employing two estimators of Shannon's entropy rate based on Lempel-Ziv and Context…
Factor analysis is a statistical technique employed to evaluate how observed variables correlate through common factors and unique variables. While it is often used to analyze price movement in the unstable stock market, it does not always…
This work employs some techniques in order to filter random noise from the information provided by minimum spanning trees obtained from the correlation matrices of international stock market indices prior to and during times of crisis. The…
We use the correlation matrix of stocks returns in order to create maps of the S\~ao Paulo Stock Exchange (BM&F-Bovespa), Brazil's main stock exchange. The data reffer to the year 2010, and the correlations between stock returns lead to the…
Using the eigenvalues and eigenvectors of correlations matrices of some of the main financial market indices in the world, we show that high volatility of markets is directly linked with strong correlations between them. This means that…
Permutation approach is suggested as a method to investigate financial time series in micro scales. The method is used to see how high frequency trading in recent years has affected the micro patterns which may be seen in financial time…
In the framework of Multifractal Diffusion Entropy Analysis we propose a method for choosing an optimal bin-width in histograms generated from underlying probability distributions of interest. The method presented uses techniques of…
Background: For complex financial systems, the negative and positive return-volatility correlations, i.e., the so-called leverage and anti-leverage effects, are particularly important for the understanding of the price dynamics. However,…
In our previous study we have presented an approach to studying lead--lag effect in financial markets using information and network theories. Methodology presented there, as well as previous studies using Pearson's correlation for the same…
Market events such as order placement and order cancellation are examples of the complex and substantial flow of data that surrounds a modern financial engineer. New mathematical techniques, developed to describe the interactions of complex…
In the past 20 years, momentum or trend following strategies have become an established part of the investor toolbox. We introduce a new way of analyzing momentum strategies by looking at the information ratio (IR, average return divided by…
In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH…
We present a careful analysis of possible issues on the application of the self-excited Hawkes process to high-frequency financial data. We carefully analyze a set of effects leading to significant biases in the estimation of the…
Modelling financial time series as a time change of a simpler process has been proposed in various forms over the years. One of such recent approaches is called volatility homogenisation decomposition, and has been designed specifically to…
This study uses hierarchical structure methods (minimal spanning tree, (MST) and hierarchical tree, (HT)) to examine the hierarchical structures of the United State (US) foreign trade by using the real prices of their commodity export and…
We investigate the hierarchical structures of countries based on electricity consumption and economic growth by using the real amounts of their consumption over a certain time period. We use of electricity consumption data to detect the…
We suggest an original physical approach to describe the mechanism of market pricing. The core of our approach is to consider pricing at different time scales separately, using independent equations of motion. Such an approach leads to a…
Many commonly used liquidity measures are based on snapshots of the state of the limit order book (LOB) and can thus only provide information about instantaneous liquidity, and not regarding the local liquidity regime. However, trading in…
We present a large-scale study of commonality in liquidity and resilience across assets in an ultra high-frequency (millisecond-timestamped) Limit Order Book (LOB) dataset from a pan-European electronic equity trading facility. We first…