Anastasios Malliaris

Differential equations, stability and chaos in dynamic economics

Basic Properties of Differential Equations. Linear Differential Equations. Stability Methods: An Introduction. Advanced Stability Methods. Stability of Optimal Control. Microeconomic Dynamics. Stability in Investment Theory. Macroeconomic Policies. Stability in Capital Theory. Introduction to Chaos and Other Aspects of Nonlinearity. Appendix. Bibliography. Index.

Searching for fractal structure in agricultural futures markets

The four parameters of the Pareto stable probability distribution for six agricultural futures are estimated. The behavior of these estimates for different time-scaled distributions is consistent with the conjecture that the stochastic processes generating these agricultural futures returns are characterized by a fractal structure. In particular, it is empirically verified that the six futures returns satisfy the property of statistical self-similarity. Moreover, the same time series is analyzed by using the so-called rescaled range analysis. This analysis is able to detect both the fractal structure and the presence of long-term dependence within the observations. The Hurst exponent with the use of two methods, the classical and modified rescaled analysis, is estimated and tested. Finally, with the use of Mandelbrot’s result on the existence of a link between the characteristic ex

Volume and price relationships: Hypotheses and testing for agricultural futures

The relationship between trading volume and price variability has been examined extensively. The theoretical motivation of earlier studies such as Ying (1966), Crouch (1970), Clark (1973), Copeland (1976), Epps and Epps (1976), Westerfield (1977), Rogalski (1978), and Upton and Shannon (1979) was the demand and supply model of microeconomic theory. Some authors have investigated the price‐volume relationship with the use of data from futures markets; these include Cornell (1981), Tauchen and Pitts (1983), Rutledge (1984), Grammatikos and Saunders (1986), Garcia, Leuthold, and Zapata (1986), and Bhar and Malliaris (1996). Other researchers have studied the determinants of volume with the use of macroeconomic and financial variables other than price variWe are thankful for useful comments to David B. Mirza, Bruce D. Phelps, and Stanley Pliska. The article has also benefited from the comments and suggestions of three anonymous referees, Professor Hector Zapata and the Editor, Mark Powers. Earlier versions of the article were presented at the Futures and Options Seminar at the University of Illinois at Chicago, and at the annual meetings of the Financial Management Association, and the Midwest Finance Association. We are grateful to our research assistant Raffaella Cremonesi, and especially to Caglar Alkan for extensive computer work.

Methodological issues in asset pricing: Random walk or chaotic dynamics

Abstract We analyze the theoretical foundations of the efficient market hypothesis by stressing the efficient use of information and its effect upon price volatility. The “random walk” hypothesis assumes that price volatility is exogenous and unexplained. Randomness means that a knowledge of the past cannot help to predict the future. We accept the view that randomness appears because information is incomplete. The larger the subset of information available and known, the less emphasis one must place upon the generic term randomness. We construct a general and well accepted intertemporal price determination model, and show that price volatility reflects the output of a higher order dynamic system with an underlying stochastic foundation. Our analysis is used to explain the learning process and the efficient use of information in our archetype model. We estimate a general unrestricted system for financial and agricultural markets to see which specifications we can reject. What emerges is that a system very close to our archetype model is consistent with the evidence. We obtain an equation for price volatility which looks a lot like the GARCH equation. The price variability is a serially correlated variable which is affected by the Bayesian error, and the Bayesian error is a serially correlated variable which is affected by the noisiness of the system. In this manner we have explained some of the determinants of what has been called the “randomness” of price changes.

Volume and Volatility in Foreign Currency Futures Markets

In this paper we propose and test several hypotheses concerning time series properties of trading volume, price, short and long-term relationships between price and volume and the determinants of trading volume in forcign currency futures. The nearby contracts for British Pound, Canadian Dollar, Japanese Yen, German Mark and Swiss Franc are analyzed in three frequencies i.e. daily, weekly and monthly.We find supportive evidence for all the five currencies that the price volatility is a determinant of the trading volume changes. Furthermore, the volatility of the price process is a determinant of the unexpected component of the changes in trading volume. Also, there is a significant relationship between the volatility of price and the volatility of trading volume changes for three of the five currencies in the daily frequency and for one currency in the monthly frequency.

An empirical investigation among real, monetary and financial variables

Abstract This paper attempts to make an empirical contribution to the literature on the relationships among real, monetary and financial variables of the economy. Using the methodology of Grangers causality tests, our results indicate that: (i) Money Supply and SP (ii) Money Supply seems to lead the S&P 500 Index and, (iii) the S&P 500 Index seems to lead the Industrial Production Index. Our findings tend to confirm the important role played by Money Supply in the economy and the popular hypothesis that stock return fluctuations are a leading indicator of future real economic activity. However, our results also show that the causal relationships among these three economic variables are not as statistically significant as the economic and financial literature suggests.

Asymptotic Growth under Uncertainty: Existence and Uniqueness

This paper demonstrates, using the Reflection Principle, the existence and uniqueness of the solution to the classic Solow equation under continuous time uncertainty for the class of strictly concave production functions which are continuously differentiable on the nonnegative real numbers. This class contains all CES functions with elasticity of substitution less than unity. A steady state distribution also exists for this class of production functions which have a bounded slope at the origin. A condition on the drift-variance ratio of the stochastic differential equation alone, independent of technology and the savings ratio, is found to be necessary for the existence of a steady state.

ITO'S CALCULUS IN FINANCIAL DECISION MAKING*

This paper presents an introduction to Ito’s stochastic calculus by stating some basic definitions, theorems and mathematical examples. Afterwards, the use of Ito’s calculus in modern financial theory is illustrated by expositing a few representative applications. The main observation of this paper is that Ito’s calculus which was developed from purely mathematical questions originating in Wiener’s work has found unexpectedly important applicability in the theory of finance from the perspective of continuous time.

New Perspectives on Asset Price Bubbles

Th e primary purpose of this book is to critically reexamine the profession’s understanding of asset price bubbles in light of the major fi nancial crisis of 2007–2009. It is well known that asset bubbles have occurred in the past, with the October 1929 stock market crash as perhaps the most demonstrative example. However, the remarkable positive performance of the U.S. economy from 1945 to 2006, and, in particular, during the Great Moderation of 1984 to 2006, suggested to the economics profession and monetary policymakers that asset bubbles could be eff ectively ignored with little or no real adverse economic impact. For example, the October 1987 one-day U.S. stock market crash of 20% did not seriously impact the real economy. Likewise, the bursting of the Internet bubble in 2000, when the NASDAQ dropped by 70% from its level of about 4,500 in early 2000 to 1,500 in April 2002, contributed only to an eight-month mild recession from March to November, 2011. In contrast to these mild real economic consequences of asset bubbles bursting, both the Great Crash of 1929, which was followed by a severe economic depression, and the crash of the Japanese stock and real estate markets that led to the so-called “lost decade” in Japan remind us that the severity of the spillover from asset bubbles bursting should not be underestimated. Th e recent fi nancial crisis of 2007–2009, which was followed by the “Great Recession” lasting 18 months from December 2007 to June 2009, has triggered a debate about what we really know about asset price bubbles and how (and whether) they can be managed in the public interest. Th ere are various components to this debate. For example, the effi cient markets hypothesis views extraordinary movements in asset prices as a consequence of signifi cant changes in information about fundamentals. Th is approach to asset pricing downplays the need to consider asset bubbles as a source of fi nancial instability. It is

How did the Fed react to the 1990s stock market bubble? Evidence from an extended Taylor rule

How did the Federal Reserve Bank react to the stock market bubble of the late 1990s? At a Symposium sponsored by the Federal Reserve Bank of Kansas City in Jackson Hole, Wyoming on August 30, 2002, Chairman Alan Greenspan remarked that economists do not currently have a way to measure a stock market bubble convincingly. He also argued that in the absence of such a measure, it was difficult for the Fed to justify, with some degree of certainty, a preemptive tightening that would likely be necessary to neutralize such a bubble. This paper extends the Taylor Rule methodology to include three measures of stock market overvaluation and confirms Greenspans statement that the Fed did not neutralize the bubble. However, the extended Taylor Rule methodology also shows that the Fed, perhaps unintentionally, by keeping the Fed funds rate below those suggested by the Taylor Rule, may have actually contributed to the growth of the bubble.