مدلسازی پویایی بازار سهام بر اساس اصول حفاظت
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|15874||2001||19 صفحه PDF||سفارش دهید||6767 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Physica A: Statistical Mechanics and its Applications, Volume 301, Issues 1–4, 1 December 2001, Pages 493–511
In this paper, a deterministic framework for modeling stock market dynamics is presented. The model is based on assets conservation principles and consists of a series of differential equations describing the dynamics of assets trading, and a (nonlinear) functional equation describing trade conservation (i.e., what is bought (sold) by one trader is sold (bought) by other traders). In this way, the dynamics of the assets and its price are determined by the trading dynamics. An equilibrium price is achieved when certain demand/supply equations are satisfied. Attention is devoted to a specific case, in which the trading activity is based on trader groups and an infinitely divisible asset. Numerical simulations show that even a single stock market asset with two classes of investors can display oscillatory price dynamics and instability. Moreover, the underlying oscillatory time-series display a discontinuous erratic-type behavior.
Since the highly original work by Bachelier , following with the deep remarks by Working  and , the contributions by Samuelson , and the subsequent work of several economists and scientists, it has been arrived to the conviction that future asset prices tend to be largely random. This belief directed many investigations to seek theories to describe and understand such phenomenon. The underlying idea is that the evolution of the price of even a single stock market asset is commonly considered as an extremely difficult object of study. To interpret the price time-series from given information and to predict future values is such a discouraging and hopeless task, that the universally accepted approach is currently of probabilistic/statistical nature . During the past 20 years, a very large literature developed concerning the statistical distribution of the changes in future prices (see for instances,  and ). In the physics literature, the statistical approach gave rise to an avalanche of publications demonstrating the application of mechanical statistical tools to explain regularities in e.g., price volatility and fundamentals . Recent issues of Physica A showcase the application of physics methodologies to understand the dynamics of stock markets. An example of application of stochastic analysis with a physics viewpoint is the description of price changes in open markets ,  and . The major problem with the statistical approach is that it is incapable of understanding the underlying dynamics governing price evolution. For instance, it is not clear how the heterogeneity and composition of agents in a stock market affect the price dynamics . Moreover, arguments based on the deepest statistical machinery seems to erode seriously the confidence of the famous Efficient Market Hypothesis and its sequel : the random walk model for prices of financial assets. This state of events has led some researchers to take alternative approaches: Is there a nonlinear methodology (e.g., deterministic models) as an alternative to the stochastic approach, which generates a time-series sequence of price changes that appear random when in fact such sequence is nonrandom? The issue of deterministic chaos to explain price volatility has been documented (see for instance,  and ). The empirical analysis on price time-series presented in the book of De Grauwe et al. was not conclusive of chaos in asset markets. Specifically, in no case could they find a strange attractor. Major criticisms have been made to the deterministic chaos models . If a model is chaotic, then short run forecasting is quite feasible, but longer run forecasting is impossible. The empirical evidence in asset price changes is just the opposite. For instance, short period (e.g., monthly or quarterly) rates of inflation cannot be predicted, but in the long run period the quantity theory of money is valid . Malliaris and Stein  have suggested that price volatility processes reflect the output of a higher-order dynamic system with an underlying stochastic foundation, and analyzed the economic scenarios which may generate seemingly chaotic processes that can be interpreted statistically. They constructed an intertemporal price determination model to explain the learning process and the efficient use of information. Based on such model, analysis on actual financial market (S&P 500) and agricultural commodities, it has been concluded that the pure random walk hypothesis of price changes is rejected. Although Malliaris and Stein's model was archetype, it can be considered as a first attempt to systematize and clarify the underlying mechanisms determining price volatility. In the spirit of Malliaris and Stein's approach, a deterministic framework for modeling stock market dynamics is presented in this paper. The model is based on assets conservation principles to reflect asset trading among different traders classes. The main goal of our modeling approach is to gain insight and understanding of the intrinsic mechanisms driving the price dynamics. To this end, a simple stock market dynamics is addressed; namely, one asset with a small number of investors types and simple trading rules. Since some universally accepted determinants of the dynamics of stock markets are psychological reactions of traders, our idea is to model some attitudes towards levels and changes of prices that make different types of investors, and to conform all together within an interaction model. The model consists of a series of differential equations describing the dynamics of asset trading among different agent groups, and a functional equation describing trade balance (i.e., what is bought (sold) by one trader is sold (bought) by another traders). In this way, the dynamics of the asset is determined by the trading dynamics. An equilibrium price is achieved when certain demand/supply equations are satisfied. Attention is devoted to a specific case, in which the trading activity is based on trader groups and a infinitely divisible asset. The applicability of the modeling framework is illustrated with a simple case of two trader classes as characterized by De Long et al. . It is shown that the resulting dynamic model is equivalent to a differential equation of neutral type  and . Numerical simulations show a variety of dynamic behaviors, ranging from simple exponential stability/instability to complex oscillatory price behaviors, which resembles the random behavior of actual price dynamics. The paper is organized as follows. Section 2 presents and discusses the modeling framework. Section 3 presents a case-study with two trader groups. Section 4 presents some numerical simulations. Section 5 closes the paper with some concluding remarks.
نتیجه گیری انگلیسی
We have presented a simple framework for continuous time modeling of stock markets dynamics. The basic model structure is of deterministic nature and consists of a set of differential equations describing the dynamics of traded assets, and (generally) nonlinear equations describing the price dynamics. The model is completed when boundary-type conditions for the agents trading task are provided. To illustrate the applicability of the modeling framework, a simple linear model was studied with some details. In this case, it was shown that the resulting equation governing the price dynamics is of neutral-type, an important kind of functional-differential equation, which can display a rich variety of dynamic behaviors, ranging from exponential stability and instability to complex oscillatory behaviors. Numerical simulations were provided to illustrate the main characteristics of the price dynamics and to interpret them in terms of stock market dynamics. The main conclusion of this paper is two-fold: (1) deterministic approach to modeling stock market dynamics can simulate price time-series with statistical characteristics similar to those in real stock market, and (2) the building blocks of such dynamics can be given by several types of observable trader behaviors. Numerical simulations presented above show that complex oscillatory behaviors can be obtained from a very simple model with two investors classes. In principle, the addition of more positive feedback traders with different expectations and estimation time-horizons would yield price dynamics with many fundamental frequencies . It is apparent that the resulting price time-series would produce strange “attractors” with very complex geometries. Moreover, discontinuities in the dynamics of neutral differential equations and heterogeneity of investors classes would make very hard short-run price forecasting, which is in agreement with early observations . Some other interesting problems can be addressed within our modeling framework. For instance, (a) The role of a central bank in price stability , (b) The effects of several positive feedback investors with (commensurate or incommensurate) time-horizons hi>0. In this case, several fundamental frequencies are expected to appear , which introduces more complexity in price dynamics, and (c) The case when the ith trader dynamics depends on actual and/or past jth trading. The modeling framework presented in this paper must be seen as a first step towards a systematic modeling of complex stock market dynamics. In fact, a more comprehensive model should be the result of research in different fields, from system theory, phycology, stochastic processes, finance, etc. In principle, only an interdisciplinary approach should provide an explanation to the central mechanisms involved in stock market dynamics.