M. Wiliński

Structural and topological phase transitions on the German Stock Exchange

We find numerical and empirical evidence for dynamical, structural and topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in the temporal vicinity of the worldwide financial crash. Using the Minimal Spanning Tree (MST) technique, a particularly useful canonical tool of the graph theory, two transitions of the topology of a complex network representing the FSE were found. The first transition is from a hierarchical scale-free MST representing the stock market before the recent worldwide financial crash, to a superstar-like MST decorated by a scale-free hierarchy of trees representing the market’s state for the period containing the crash. Subsequently, a transition is observed from this transient, (meta)stable state of the crash to a hierarchical scale-free MST decorated by several star-like trees after the worldwide financial crash. The phase transitions observed are analogous to the ones we obtained earlier for the Warsaw Stock Exchange and more pronounced than those found by Onnela–Chakraborti–Kaski–Kertesz for the S&P 500 index in the vicinity of Black Monday (October 19, 1987) and also in the vicinity of January 1, 1998. Our results provide an empirical foundation for the future theory of dynamical, structural and topological phase transitions on financial markets.

An analysis of price impact functions of individual trades on the London stock exchange

Price impact is an important area of research in market microstructure. Previous studies have examined the relationship between trade size and price impact on a number of equity markets. In this study, using recent order book data from the London Stock Exchange, we examine the immediate price impact function for all stocks from FTSE 100 and novelly we investigate whether the function displays time-of-day effects. The results show that price impact exhibits a power-law scaling that price impact is highest in the first hour of the trading day, and lowest in the 90 minutes before market close.

Intra-day variability of the stock market activity versus stationarity of the financial time series

In this paper we propose a new approach to a well-known phenomena of intra-day activity pattern on the stock market. We suggest that seasonality of inter-transaction times has a more significant impact than intra-day pattern of volatility. Our aim is not to remove the intra-day pattern from the data but to describe its impact on autocorrelation function estimators. We obtain an exact, analytical formula relating estimators of the autocorrelation functions of non-stationary (seasonal) process to its stationary counterpart. Hence, we prove that the day seasonality of inter-transaction times extends the memory of the process. That is, autocorrelation of both, price returns and their absolute values, relaxation to zero is longer.

Can banks default overnight? Modelling endogenous contagion on the O/N interbank market

We propose a new model of the liquidity-driven banking system focusing on overnight interbank loans. This significant branch of the interbank market is commonly neglected in the banking system modelling and systemic risk analysis. We construct a model where banks are allowed to use both the interbank and the securities markets to manage their liquidity demand and supply as driven by prudential requirements in a volatile environment. The network of interbank loans is dynamic and simulated every day. We show how the intrasystem cash fluctuations alone, without any external shocks, may lead to systemic defaults, and what may be a symptom of the self-organized criticality of the system. We also analyze the impact of different prudential regulations and market conditions on the interbank market resilience. We confirm that the central bank’s asset purchase programmes, limiting the declines in government bond prices, can successfully stabilize banks’ liquidity demands. The model can be used to analyze the interbank market impact of macroprudential tools.

Complex Correlation Approach for High Frequency Financial Data

We propose a novel approach that allows to calculate Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance. Its most important feature is the ability to take into account lead-lag relations on different scales, without knowing them in advance. We also present results obtained with this approach while working on Tokyo Stock Exchange intraday quotations. We show that individual sectors and subsectors tend to form important market components which may follow each other with small but significant delays. These components may be recognized by analysing eigenvectors of complex correlation matrix for Nikkei 225 stocks. Interestingly, sectorial components are also found in eigenvectors corresponding to the bulk eigenvalues, traditionally treated as noise.

An analysis of price impact functions of individual trades on the London Stock Exchange

Studying price impact is important in finance and previous work examines the relationship between trade size and price impact on a number of equity markets. In this study, using recent order book data from the London Stock Exchange, we examine the price impact function for six highly-liquid stocks and novelly investigate whether the function displays time-of-day effects. The results show that price impact exhibits a power-law scaling, and that price impact is highest in the first hour of the trading day and lowest in the last ninety minutes of trading.