Realizing stock market crashes: stochastic cusp catastrophe model of returns under the time-varying volatility

This paper develops a two-step estimation methodology, which allows us to apply catastrophe theory to stock market returns with time-varying volatility and model stock market crashes. Utilizing high frequency data, we estimate the daily realized volatility from the returns in the first step and use stochastic cusp catastrophe on data normalized by the estimated volatility in the second step to study possible discontinuities in markets. We support our methodology by simulations where we also discuss the importance of stochastic noise and volatility in deterministic cusp catastrophe model. The methodology is empirically tested on almost 27 years of U.S. stock market evolution covering several important recessions and crisis periods. Due to the very long sample period we also develop a rolling estimation approach and we find that while in the first half of the period stock markets showed marks of bifurcations, in the second half catastrophe theory was not able to confirm this behavior. Results suggest that the proposed methodology provides an important shift in application of catastrophe theory to stock markets

Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog

The Premium of Marine Protected Areas: A Simple Valuation Model

The article addresses the induced cost, the premium, from establishing a marine protected area in a deterministic model of a fishery. Outside the protected area, the fishery is managed optimally through total allowable catch quotas. The premium is found to be increasing and convex along the protection parameter. Biological measures are introduced to increase the understanding of the mechanisms in the bioeconomic system. Time-series solutions show that the net return per unit of fish increases after the protected area is established.Bioeconomics, dynamic programming, fisheries management, marine protected areas, migration, modeling, optimization, renewable resources., International Development, International Relations/Trade, Political Economy, Research and Development/Tech Change/Emerging Technologies, C61, Q22, Q57.,

How Can We Define The Concept of Long Memory? An Econometric Survey

In this paper we discuss different aspects of long mzmory behavior and specify what kinds of parametric models follow them. We discuss the confusion which can arise when empirical autocorrelation function of a short memory process decreases in an hyperbolic way.Long-memory, Switching, Estimation theory, Spectral

Analysing divergent logistic networks with local (R, S) inventory control

This paper deals with divergent logistic networks where the inventory at each node is controlled using a periodic review strategy with order-up-to level. An approximate method is presented to analyse the network performance (service levels, mean physical stock). The method is tested on a range of 2-echelon and 3-echelon networks by comparison to results from Monte Carlo simulation. We conclude that the approximation accuracy is sufficient for global network design in many practical situation

Linear stochastic dynamics with nonlinear fractal properties

Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with multiplicative noise produce intermittency of a special kind, characterized by a power law probability density distribution. We present a review of applications on population dynamics, epidemics, finance and insurance applications with relation to ARCH(1) process, immigration and investment portfolios and the internet. We highlight the common physical mechanism and summarize the main known results. The distribution and statistical properties of the duration of intermittent bursts are also characterized in details.Comment: 26 pages, Physica A (in press

A selective overview of nonparametric methods in financial econometrics

This paper gives a brief overview on the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inferences of instantaneous returns and volatility functions of time-homogeneous and time-dependent diffusion processes, and estimation of transition densities and state price densities. We first briefly describe the problems and then outline main techniques and main results. Some useful probabilistic aspects of diffusion processes are also briefly summarized to facilitate our presentation and applications.Comment: 32 pages include 7 figure

A look at the relationship between industrial dynamics and aggregate fluctuations

The firmly established evidence of right-skewness of the firms’ size distribution is generally modelled recurring to some variant of the Gibrat’s Law of Proportional Effects. In spite of its empirical success, this approach has been harshly criticized on a theoretical ground due to its lack of economic contents and its unpleasant long-run implications. In this chapter we show that a right-skewed firms’ size distribution, with its upper tail scaling down as a power law, arises naturally from a simple choice-theoretic model based on financial market imperfections and a wage setting relationship. Our results rest on a multi-agent generalization of the prey-predator model, firstly introduced into economics by Richard Goodwin forty years ago.Firm size; Prey-predator model; Business Fluctuations