Stochastic Interacting Financial Price Model And Fluctuation Characteristic Analysis

For a long time,asset pricing theory and price fluctuation characteristics in financial markets have been the focus of economic and financial researchers.Especially in recent years,with the liberalization and diversification of the world economic environment and the fast expansion of information technology,the complexity,randomness and dynamics of financial markets have become increasingly prominent.It is increasingly important to conduct innovative research on the price fluctuation behavior and characteristics of financial markets from multiple perspectives.Many abnormal fluctuations in financial markets are difficult to be fully explained by traditional finance theories,so it becomes necessary to seek models that can better grasp the essential attributes of financial markets.Scholars’ research on the real market is gradually shifting to nonlinearity or dynamics,which leads to the emergence and development of interdisciplinary.This paper integrates the concepts,methods and theories of statistical physics,complex systems science,nonlinear science,applied mathematics,financial engineering,econometrics and other disciplines to model the change rules of asset price fluctuations in financial markets.At the same time,through computer simulation and abundant empirical research,this paper aims to reproduce the typical characteristics of price fluctuations in the financial market,discover the common law of price fluctuation behavior,explain the micro mechanism of price fluctuation formation,and provide theoretical support for preventing excessive market fluctuations and resolving financial risks.Specifically,the innovation research content of this paper is as follows:In order to explore the dynamic evolution mechanism formed by investors’ micro-interaction and interaction level,this article borrows the complex action mechanism between particles in the statistical physics system to simulate the process of interaction between investors.This article establishes two new random interactive financial prices Agent-based models that reflect the nature of the financial market.The main idea is to consider that the financial market and physical system are also complicated adaptive systems,both consisting of a large number of micro agents(subjects).These subjects interact with each other,and eventually show collective emergence and generate macro complex phenomena.This subject,in the financial market,refers to investment decision makers that can exchange information and participate in asset transaction decisions,including individual investors and institutional investors;in physical systems,it is manifested as particles that can interact or interactive metastasis.Most investors in the financial market are affected by the herd effects.Different investment attitudes,good messages and negative news information,buying decisions and selling decisions spread among market participants.These will affect the power ratio of market demand and supply,and eventually lead to changes in asset prices.This evolution can be described by random interaction between particles in the statistical physics system.Specifically,the interaction behavior between particles is used to describe information dissemination and mutual influence behavior between investors,and changes in particle state are used to simulate the changes in investors’ investment decisions.The establishment of Agent-Based random interaction financial price model is a bottom-up research method.It abstracts the real market participants and uses computer simulation to make research no longer stay at the macro market level.This method can explain the micro causes of some macro phenomena of price fluctuations and its specific evolutionary process.Firstly,this paper introduces the multitype contact process and the oriented percolation in the statistical physical system,and establishes a new stochastic interacting financial price model I with jump.In the research process,the heterogeneity of agents’ investment attitudes is added to make model more suitable for the actual market than the previous research based on the single particle contact process.The interaction among agents and the dynamic change of investment attitude and investment strategy are simulated by the complex interaction among particles of different states in the multitype contact process,which lead to the frequent and normal fluctuations.The multitype contact process can be described by the transmission process of viruses with different infectivity rates among individuals,which is similar to the exchange of attitude and strategy among agents with different investment attitudes in financial markets.Secondly,in order to describe the market price dynamics more comprehensively,the new model constructed in this paper not only simulates the frequent and normal fluctuations of financial markets,but also takes into account the sudden and violent price fluctuations of markets.For sudden and violent fluctuations of financial markets,the model adopts the oriented percolation combined with Poisson process to simulate this part of price jump process.The flow and filtration process of the oriented percolation after the injection of liquid is similar to the herd behavior that agents interact with each other when facing significant information.Therefore,the oriented percolation is used to construct the demand formation mechanism and simulate the amplitude of price jump.The frequency of price jumps is described by the homogeneous Poisson process.The introduction of random jump factor in the modeling process makes it more comprehensive for the description of asset price changes.Thirdly,in order to explore the influence of information network exchange channel structure on price change rules,this paper combines the establishment mechanism of price process with social network to establish the stochastic interacting financial price model II.This model creatively expands the range of connection among market participants from regular lattice to Watts-Strogatz small-world network which is more consistent with the real market characteristics.This innovative work takes into account the more complex information exchange and attitude sharing among market agents,and the more diverse ways investors obtain information.The rich and complex connections in the small-world network will affect the interaction amomg agents and the price dynamics of financial markets.In this paper,the network structure is combined with the information exchange mechanism among agents,which links the financial price fluctuation behavior with the topology of information exchange channel among market participants.The above consideration of the connection structure and communication range of market agents is a new supplement to the theoretical research in related fields.Fourthly,after the price process theory,to validate the rationality of the models from empirical angle and deeply explore the fluctuation characteristics of financial markets,this paper introduces a large number of methods that can deeply explore the inherent characteristics of financial time series,and comprehensively compares and analyzes the simulated data generated by the two models with the real market data.For example,this paper performs an exploration of basic statistical characteristics,power-law scaling property,long memory,volatility cluster,zipf law,multi-fractal property,complexity behavior,chaotic property,etc.In the empirical process,through the discussion of several important parameters in the models,it is found that the change of parameters will have an impact on the price fluctuation dynamics,including the transmission rate of the investment decision of the agents with a strong investment attitude,the amplitude and frequency of price jump,and the connection probability of the information exchange network channel.Abundant empirical comparative analysis shows that the simulated data and real data have similar fluctuation characteristics,which proves that this paper establishes the stochastic interacting financial price model that can reproduce the basic characteristics of the real market,and discusses the laws of the price fluctuation characteristic of financial markets in depth.In summary,this paper constructs the new stochastic interacting financial price models that can reflect the essential features of financial markets,and explain the microscopic mechanism of the formation of price fluctuations from the perspectives of market participants’ information interaction,emotional infection and network connection structure.At the same time,this paper demonstrates the feasibility of the model from the perspective of theoretical construction and empirical analysis,which can be applied to the simulation of real financial markets.Model I focuses on the description of the gradual spread and penetration of investment information or attitudes among different types of investors in the local area to influence price changes.Different starting points of information transmission will lead to different ranges of transmission and influence,which may lead to different price behavior.The research focus of Model II is to combine the establishment process of price mechanism with the connection structure of market participants,highlight the impact of network connectivity efficiency of information exchange on price dynamics,expand the interactive influence range of investors,and have the characteristics of systemic impact and rapid dissemination of news.The reasonable modeling and abundant empirical analysis results of the price dynamics of financial markets in this paper can help researchers to explore the micro mechanism of price fluctuations and make optimal decisions.It can also bring important enlightenment for regulators to formulate reasonable policies and promote the stable development of financial market,which is of great practical significance to China’s stock market with frequent fluctuations.