Abstract: This paper focuses on the dynamical aspects of systemic risk in financial markets resulting from positive feedback loops in the interaction of risk management and asset markets. It will thereby highlight the importance of non-equilibrium approaches to understanding and tackling systemic risk in financial markets. We investigate a simple dynamical model for the systemic risk caused by the use of Value-at-Risk (VaR). The model consists of a bank with a leverage target and an unleveraged fundamentalist investor subject to exogenous noise with clustered volatility. The parameter space has three regions: (i) a stable region, where the system has a fixed point equilibrium; (ii) a locally unstable region, characterized by cycles with chaotic behavior; and (iii) a globally unstable region. A calibration of parameters to data puts the model in region (ii). In this region there is a slowly building price bubble, resembling the period prior to the Global Financial Crisis, followed by a crash resembling the crisis, with a period of approximately 10–15 years. While our model does not show that the financial crisis and the period leading up to it were due to VaR risk management policies, it does suggest that it could have been caused by VaR risk management, and that the housing bubble may have just been the spark that triggered the crisis. We also explore alternative leverage control policies based on their ability to minimize risk for a given average leverage. We find the best policy depends on the market impact of the bank. VaR is optimal when the exogenous noise is high, the bank is small and leverage is low; in the opposite limit where the bank is large and leverage is high the optimal policy is closer to constant leverage.

Abstract: On September 15, 2008, the Lehman Brothers bank announced its bankruptcy. This started a panic on the US stock exchange and the mortgage crisis that has spread throughout the world. The consequences of these events are still visible today. Since the events of 2008, concepts such as systemic risk and financial contagion are in the common language. At the same time the development of models of the interbank market has gained tremendous momentum. We want to present a new model of banking system, focusing on daily time-scale and short-term activities, mainly overnight loans. In our model we take into account three possible ways of financial contagion. The first, most direct way of propagation is by a collapsing bank not paying its obligations. Banks that granted loans bear this loss, which worsens their financial situation. Other, perhaps less obvious, a falling bank, in order to pay its obligations, must sell its external assets in significant amounts, what results in an immediate and significant decrease in their value. Not only does it not recover the full value of the assets and repays liabilities to a smaller extent, it also affects the decrease in the value of assets held in the portfolios of other banks - worsening their situation. Last, but not least, there is the decline in the availability of interbank loans due to a decrease in trust. This results in banks having lower resistance to deterioration of their financial situation. Most of the previous models tested the system's reaction to an external shock e.g. collapse of one or more banks. In contrast, in our dynamical model of the entire banking system crashes can occur as an internal feature of the system. We will present results for artificial data as well as for empirical data from Polish interbank market.

Abstract: The amount of data has been radically increasing accompanied by the development of electronics devices, and the data set, so-called big data has attracted attention among econophysicists lately. One of the field where big data becomes available is foreign exchange market (FX market). The big data of FX market is called as the Order Book Data and it includes the data described below: i. Transaction price from start to end of the FX market ii. Order volume and order price of traders iii. Time when traders put an order and cancel it It is reported that there is a correlation between transaction price movement and behavior of traders, and its sign changes depending on which price range trader put an order at(Ref.[1,2]). The correlation implies that price movement and trader behavior are closely related and its relation enable us to understand the various property of price movement from traders behavior, including a sudden jump of price. There, however, have been few studies on the correlation between price movement and trader behavior. We study the statistical properties of traders behavior so as to understand that relation. We focus on the relaxation process for trader's order and report that there is a typical pattern for relaxation timescale, and it depends on which price range they are　at. This result is consistent with the one shown by [2]. References [1] Y.Yura, H.Takayasu, D.Sornette, M.Takayasu, Physical Review E 92.4 (2015): 042811. [2] Y. Yura, H.Takayasu, D.Sornette, M.Takayasu, Phys. Rev. Lett. 112, 098703 (2015).

Abstract: We propose a network-based similarity measure between portfolios with possibly very different numbers of assets and apply it to a historical database of institutional holdings ranging from 1999 to the end of 2013. The resulting portfolio similarity measure increased steadily before the 2008 financial crisis and reached a maximum when the crisis occurred. We argue that the nature of this measure implies that liquidation risk from fire sales was maximal at that time. After a sharp drop in 2008, portfolio similarity resumed its growth in 2009, with a notable acceleration in 2013, reaching levels not seen since 2007.

Abstract: Few attempts have been proposed in order to describe the statistical features and historical evolution of the export bipartite matrix countries/products. An important standpoint is the introduction of a products network, namely a hierarchical forest of products that models the formation and the evolution of commodities. In the present article, we propose a simple dynamical model where countries compete with each other to acquire the ability to produce and export new products. Countries will have two possibilities to expand their export: innovating, i.e. introducing new goods, namely new nodes in the product networks, or copying the productive process of others, i.e. occupying a node already present in the same network. In this way, the topology of the products network and the country-product matrix evolve simultaneously, driven by the countries push toward innovation.