Nonlinearity in the dynamics of financial markets

A new set of methodologies extracts key nonlinearities in the dynamics of financial markets from data that would appear to be completely random with ordinary linear time series methods. The understanding acquired from this analysis forms a basis for modeling conflicting and competing motivations in market decisions. By standardizing the daily changes using the mean and standard deviation, it then becomes possible to compare the quantitative impact of very different variables such as price trend and valuation, and the nonlinear relationship between them. The analysis of a large data set of closing stock prices provides strong statistical evidence that relative daily price change is positively influenced by valuation, recent price trend, short term volatility, volume trend and the M2 money supply. However, there is a strong nonlinearity in the influence of the price trend, so that a significantly large recent uptrend has a negative influence on the subsequent day’s relative price change. The nonlinearity is the key to understanding the conflicting role of price trend, since a single large data set exhibits both underreaction and overreaction in different regimes of the independent variables. The role of long term volatility is not a clear-cut risk/return inverse relation. But rather there is an ambiguous and complicated relationship between volatility and return. There is limited support for resistance when prices near the quarterly high. Mixed effects regressions are used after standardizing the data by subtracting the mean and dividing by one standard deviation individually for each of the 119 closed-end funds. A valuation variable is constructed in terms of the recent history of net asset value.     

Pseudochaotic dynamics near global periodicity

In this paper, we study a piecewise linear version of kicked oscillator model: saw-tooth map. A special case of global periodicity, in which every phase point belongs to a periodic orbit, is presented. With few analytic results known for the corresponding map on torus, we numerically investigate transport properties and statistical behavior of Poincaré recurrence time in two cases of deviation from global periodicity. A non-KAM behavior of the system, as well as subdiffusion and superdiffusion, are observed through numerical simulations. Statistics of Poincaré recurrences shows Kac lemma is valid in the system and there is a relation between the transport exponent and the Poincaré recurrence exponent. We also perform careful numerical computation of capacity, information and correlation dimensions of the so-called exceptional set in both cases. Our results show that the fractal dimension of the exceptional set is strictly less than 2 and that the fractal structures are unifractal rather than multifractal.     

On the global dynamics of periodic triangular maps

This paper is an extension of an earlier paper that dealt with global dynamics in autonomous triangular maps. In the current paper, we extend the results on global dynamics of autonomous triangular maps to periodic non-autonomous triangular maps. We show that, under certain conditions, the orbit of every point in a periodic non-autonomous triangular map converges to a fixed point (respectively, periodic orbit of period p) if and only if there is no periodic orbit of prime period two (respectively, periodic orbits of prime period greater than p).     

Classes of network connectivity and dynamics

Many kinds of complex systems exhibit characteristic patterns of temporal correlations that emerge as the result of functional interactions within a structured network. One such complex system is the brain, composed of numerous neuronal units linked by synaptic connections. The activity of these neuronal units gives rise to dynamic states that are characterized by specific patterns of neuronal activation and co‐activation. These patterns, called functional connectivity, are possible neural correlates of perceptual and cognitive processes. Which functional connectivity patterns arise depends on the anatomical structure of the underlying network, which in turn is modified by a broad range of activity‐dependent processes. Given this intricate relationship between structure and function, the question of how patterns of anatomical connectivity constrain or determine dynamical patterns is of considerable theoretical importance. The present study develops computational tools to analyze networks in terms of their structure and dynamics. We identify different classes of network, including networks that are characterized by high complexity. These highly complex networks have distinct structural characteristics such as clustered connectivity and short wiring length similar to those of large‐scale networks of the cerebral cortex. © 2002 Wiley Periodicals, Inc.     

Nonlinear dynamics and chaos in a fractional-order financial system

This study examines the two most attractive characteristics, memory and chaos, in simulations of financial systems. A fractional-order financial system is proposed in this study. It is a generalization of a dynamic financial model recently reported in the literature. The fractional-order financial system displays many interesting dynamic behaviors, such as fixed points, periodic motions, and chaotic motions. It has been found that chaos exists in fractional-order financial systems with orders less than 3. In this study, the lowest order at which this system yielded chaos was 2.35. Period doubling and intermittency routes to chaos in the fractional-order financial system were found.     

Rollover risk and endogenous network dynamics

Using a dynamic network formation model, solved numerically, we study banks’ rollover decisions. We find that when the existence of linkages between market participants generates an informational externality, the newly formed network is conditioned by past architectures. Moreover, this inertia is strongly dependent on macroeconomic conditions, such as investors’ risk appetite. Simulations show that for intermediate values of the risk appetite’s parameter the financial network exhibits tipping points, i.e., the inability to maintain a threshold number of linkages may push the market into a gridlock. In this context, we study also how policy instruments, such as taxes and subsidies, affects debt rollover. Since a reduction in the policy level plays the same role as an improvement in economic fundamentals, the creation of interbank connections can be stimulated by it. Thus, in order to restart lending after a major stress situation in the interbank market a considerable reduction in the policy level is required, advising a counter-cyclical policy similar to the ones recently proposed with respect to capital requirements.     

Approximately invariant manifolds and global dynamics of spike states

We investigate the existence of a true invariant manifold given an approximately invariant manifold for an infinite-dimensional dynamical system. We prove that if the given manifold is approximately invariant and approximately normally hyperbolic, then the dynamical system has a true invariant manifold nearby. We apply this result to reveal the global dynamics of boundary spike states for the generalized Allen–Cahn equation.     

Spectral representations and global maps of cellular automata dynamics

We present a spectral representation of any computation performed by a Cellular Automaton (CA) of arbitrary topology and dimensionality via an appropriate coding scheme in Fourier space that can be implemented in an analog machine ideally circumventing part of the overall waste heat production. We explore further consequences of this encoding and we provide a simple example based on the “Game-of-Life” where we find global maps for small lattices indicating an interesting underlying recursive structure.     

On global stability of the intra-host dynamics of malaria and the immune system

In this paper we consider an intra-host model for the dynamics of malaria. The model describes the dynamics of the blood stage malaria parasites and their interaction with host cells, in particular red blood cells (RBC) and immune effectors. We establish the equilibrium points of the system and analyze their stability using the theory of competitive systems, compound matrices and stability of periodic orbits. We established that the disease-free equilibrium is globally stable if and only if the basic reproduction number satisfies R₀?1 and the parasite will be cleared out of the host. If R₀>1, a unique endemic equilibrium is globally stable and the parasites persist at the endemic steady state. In the presence of the immune response, the numerical analysis of the model shows that the endemic equilibrium is unstable.     

Hierarchical facility network planning model for global logistics network configurations

This paper presents a novel hierarchical network planning model for global logistics (GLs) network configurations. The proposed method, which is based on the fundamentals of integer programming and hierarchical cluster analysis methods, determines the corresponding locations, number and scope of service areas and facilities in the proposed GLs network. Therein, a multi-objective planning model is formulated that systematically minimizes network configuration cost and maximizes both operational profit and the customer satisfaction rate. Particularly, potential risk-oriented costs, such as macro-environmental-risk and micro-operational-risk costs are considered in the proposed model. Numerical results indicate that the overall system performance can be improved by up to 11.52% using the proposed approach.     

On the global dynamics of attractors for scalar delay equations

A semi-conjugacy from the dynamics of the global attractors for a family of scalar delay differential equations with negative feedback onto the dynamics of a simple system of ordinary differential equations is constructed. The construction and proof are done in an abstract setting, and hence, are valid for a variety of dynamical systems which need not arise from delay equations. The proofs are based on the Conley index theory.

     

Financial contagion: extending the exposures network of the Mexican financial system

Direct contagion has been widely studied in recent years and little evidence has been found to be relevant to the study of systemic risk. However, we argue that this limited contagion effect might be associated with a lack of relevant data. A common assumption for the estimation of the matrices of exposures is to apply the maximum entropy principle to deal with data gaps; such an assumption might lead to an underestimation of contagion risk. In this paper, there are no data gaps and the information set is extended from interbank exposures alone to exposures among most of the financial intermediaries in the Mexican financial system (we even include exposures to some international foreign banks). Naturally, the contagion risk of an extended network of exposures changes with respect to the interbank exposures network, as there are many more institutions which can be the source of contagion and there are more institutions which can fail due to contagion. The most important contribution of this paper is that it provides evidence on financial contagion with an extended exposures network under stressful conditions. The results presented here support the international efforts by the Bank for International Settlements, the International Monetary Fund and the Financial Stability Board to increase the amount of information available which can be used to assess systemic risk and contagion based on exposures and funding data.     

Periodicity and global dynamics of an impulsive delay Lasota-Wazewska model

The periodicity of an impulsive delay Lasota-Wazewska model is discussed. Sufficient and necessary condition for the existence of a positive periodic solution is established. Sufficient conditions for its global attractivity are also obtained via the methods of Lyapunov function and comparison.     

Identifying systemically important financial institutions: a network approach

Computational Management Science - The Basel Committee on Banking Supervision has proposed a methodology to identify Systemically Important Financial Institutions based on a series of indicators...     

Closed-loop supply chain network design: A financial approach

The more common approaches used in the SCM consider only the physical logistic operations and ignore the financial aspects of the chain. This paper presents a financial approach to model a closed-loop supply chain design in which financial aspects are explicitly considered as exogenous variables. The model decides to determine the strategic decisions as well as the tactical decisions. The main contribution of this paper is to incorporate the financial aspects (i.e. current and fixed assets and liabilities) and a set of budgetary constraints representing balances of cash, debt, securities, payment delays, and discounts in the supply chain planning. Moreover, the financial approach applies the change in equity (instead of the measure of profit/cost in traditional approaches) as the objective function to be optimized in the presented model.To show the advantages of the presented approach, the results attributed to the financial approach and the traditional approach are compared, where the latter firstly decides on operations and fits finances afterwards. The results indicate that the traditional approach leads to lower change in equity compared to the financial approach. This fact illustrates the inadequacy of treating process operations and finances in isolated environments and pursuing as objective myopic performance indicators such as profit or cost. Moreover, a sensitivity analysis of the parameters using ANOVA for different levels of the parameters under different customer order patterns is performed to enhance the managerial insights of the study. The results clearly reveal the better improvement of using the financial approach over the traditional approach, and convince the decision makers to take advantage of the proposed approach.     

The network structure and systemic risk in the global non-life insurance market

This paper contributes to the literature on systemic risk by assessing the systemic importance of insurers in the global non-life insurance market. First, we estimate the bilateral reinsurance claims matrix using the aggregate outstanding reinsurance data from ISIS and theoretically analyze the interconnectedness in the global reinsurance network using network indicators. The robustness of the estimated matrix is fully assured by sensitivity analysis. Second, we theoretically analyze the contagious defaults introducing the Eisenberg–Noe framework. Reinsurers play a dominant role in the reinsurance network and most of them are included in our data sample. The network analysis finds that some reinsurers with large centrality measures are central in the hierarchical structure of the network. The default analysis shows the occurrences of many stand-alone defaults and only one contagious default via the global reinsurance network after the global financial crisis. In addition, one stress test based on a hypothetical severe stress scenario predicts a few occurrences of contagious defaults in the future. It follows from these analyses that systemic risk via the global reinsurance network is relatively restricted in the global non-life insurance market. In conclusion, our methodology would help supervisory authorities develop an assessment approach for interconnectedness in the global reinsurance network and aid the implementation of insurer stress tests for default contagion.     

Exploring the dynamics of financial markets: from stock prices to strategy returns

Exploring the dynamics of financial time-series is an exciting and interesting challenge because of the many truly complex interactions that underly the price formation process. In this contribution we describe some of the anomalous statistical features of such time-series and review models of the price dynamics both across time and across the universe of stocks. In particular we discuss a non-Gaussian statistical feedback process of stock returns which we have developed over the past years with the particular application of option pricing. We then discuss a cooperative model for the correlations of stock dynamics which has its roots in the field of synergetics, where numerical simulations and comparisons with real data are presented. Finally we present summarized results of an empirical analysis probing the dynamics of actual trading strategy return streams.     

Neural network calibrated stochastic processes: forecasting financial assets

If a given dynamical process contains an inherently unpredictable component, it may be modeled as a stochastic process. Typical examples from financial markets are the dynamics of prices (e.g. prices of stocks or commodities) or fundamental rates (exchange rates etc.). The unknown future value of the corresponding stochastic process is usually estimated as the expected value under a suitable measure, which may be determined from distribution of past (historical) values. The predictive power of this estimation is limited by the simplifying assumptions of common calibration methods. Here we propose a novel method of “intelligent” calibration, using learning (2-layer) neural networks in order to dynamically adapt the parameters of a stochastic model to the most recent time series of fixed length (memory depth) to the past. The process parameters are determined by the weights of the intermediate layer of the neural network. The final layer combines these parameters in a meaningful manner yielding the forecasting value for the stochastic process. On each actual finite memory, the neural network is trained by back-propagation, obtaining a much more flexible and realistic parameter calibration than an analogous fit to an autoregressive models could do. In the context of processes related to financial assets, the final combination of the output layer relates to their market-price-of-risk. The back propagation is limited to the typical memory length of the financial market (for example 10 previous business days). We demonstrate the learning efficiency of the new algorithm by tracking the next-day forecasts with one typical examples each, for the asset classes of currencies and stocks.