The modern financial system exhibits high complexity due to the interaction of various individuals and elements, and this complexity often leads to collective behavior effects that far exceed the simple summation of individual behavior effects. Traditional financial theories and mathematical modeling tools typically involve idealized, linear, and formalized assumptions, which significantly limit their ability to describe the com- plexity of real financial systems. In contrast, systems science and complexity science provide new methods and tools for studying complex financial systems. The pricing processes of assets, as one of the most critical observation targets of the financial sys- tem, represent market risks and uncertainties, which are concrete manifestations of fi- nancial complexity. These processes offer a point of entry for exploring the underlying laws of complex phenomena. Therefore, this paper will discuss asset pricing theory and its application from the perspectives of systems science and complexity science, aiming to better address the challenges that complexity brings to financial risk management.
This paper observes the persistence of price jumps in financial asset prices, which contradicts the instantaneous jump assumption in traditional jump-diffusion model of asset pricing. Therefore, based on the specific observation of jump persistence, this paper aims to propose a new theoretical and methodological framework for asset pric- ing. This framework contains three main parts, with the core being the persistent-jump- diffusion model of prices. This model provides an abstract description of the macro- scopic changes in prices and offers theoretical guidance for the other two parts. Fur- thermore, the second part of the system discusses the intrinsic generation mechanisms of prices at the micro-market-structure level, exploring the causes of the phenomenon of jumps with persistence from the evolutionary process of traders’ behavior in the market. Lastly, the framework encompasses application research considering jump persistence in three areas: jump testing, market risk measurement and prediction, and early warning of systematic market risks, to fully demonstrate the rationality of the persistent-jump- diffusion theory, revealing its significance in enhancing the effectiveness of financial risk tools and improving risk management capabilities.
This paper first proposes a persistent-jump-diffusion model for the price process,
which retains the assumption of continuous price changes from the jump-diffusion model and characterizes the jump process with persistence using a filtered Poisson pro- cess (shot noise process). This theoretical model emphasizes that the impact of a single jump on the price process is time-varying rather than instantaneous. For this special form of jump process, the paper also proposes a corresponding parameter estimation method. Subsequently, through two simulation experiments, the paper demonstrates that the persistent-jump-diffusion model can generate price sequences with financial stylized facts, and the parameter estimation method remains robust when estimating jump processes with noise. This proves the basic effectiveness and operability of the persistent-jump-diffusion theoretical model. Up to now, there has been no related re- search describing the price process from the perspective of jump persistence, making this theoretical model pioneering in its significance.
Secondly, by establishing an agent-based model of heterogeneous agents, based on the micro-structure of continuous double auction, the paper explores the impact of the trading behaviors of three types of traders—fundamental traders, chartists, and ran- dom traders—on the price formation, revealing the intrinsic generation mechanism of prices and the possible reasons for the occurrence of jumps with persistence. Based on relevant theories from behavioral economics, this paper considers the situation where traders’ confidence is shattered by extreme losses, thereby allowing fundamental traders and chartists to switch to random traders. By observing the evolution process of the number of agents and its feedback on prices, this paper draws a basic conclusion: when chartists and random traders oust fundamental traders and make their number drops to zero, persistent jumps occur more frequently.From this, it can be seen that maintaining the liquidity of fundamental traders is key to maintaining relative stability in the market.
Finally, the paper applies the theory of jump persistence to risk identification, mea- suring and predicting the magnitude of market risk, and early warning of the timing of future systematic market risks. (1) In risk identification, through Monte Carlo simula- tions, the paper reveals the limitations of traditional jump tests based on the instanta- neous jump assumption and proposes improved jump test methods. At the same time, jumps with overlapping persistence windows are considered as co-jumps, and the rules for determining co-jumps have been improved. The paper conducts empirical studies based on the SSE 50 Index and its constituent stocks, showing that the improved jump test procedures can identify more systematic co-jumps than traditional methods, indicating that the frequency of systematic risks is higher than imagined and deserves the at- tention of risk management institutions and individuals. (2) In terms of market risk mea- surement and prediction, the paper makes one-step predictions for high-frequency jump processes that follow the filtered Poisson process, obtaining improved high-frequency price forecasts and improved realized volatility, ultimately resulting in improved Value- at-Risk (VaR) and improved Expected Shortfall (ES) models. Based on historical data of the Shanghai Securities Composite Index and Shenzhen Securities Component Index, the paper empirically shows that the VaR and ES models based on the jump persistence can more accurately capture the market’s tail risks, demonstrating their statistical ad- vantages in a series of back-testing. (3) In early warning of systematic market risks, the paper combines methods from the nonlinear field for determining event synchro- nization and tools from complex networks to build a risk network based on the lead-lag relationships of exceedances, and proposes a structural indicator based on the network’s topology to measure the likelihood of systematic market risk in the future. Empirical results based on the Shanghai Securities Composite Index and its constituent stocks, and results based on the Standard & Poor’s 500 and its constituent stocks show that more than 70% of systematic market risks can be successfully predicted within the predicted intervals provided by leading stocks. Thus far, the persistent-jump-diffusion theory has been proven to be widely applicable in the field of risk management, demonstrating its advantages in forecasting, handling, and preventing extreme financial risks.
In summary, this paper follows the paradigm of “specific-general-specific”. Based on the specific phenomenon of jump persistence, a persistent-jump-diffusion pricing theory is proposed, along with a generalized mathematical model describing the laws of price movement and a generalized mechanism model explaining the intrinsic generation process of prices. Furthermore, specific application has been conducted based on this new theory, ultimately forming a new theoretical and methodological framework for asset pricing. The paper seeks to view the core problems of the financial field from the perspective of complex systems science, using a series of interdisciplinary tools to solve practical problems, to promote innovation and development in financial management theory, and ultimately achieve the practical goals of timely risk identification, early warning, control of risk losses, and prevention of financial crises.
谷歌
