Computational Experiments Successfully Predict the Emergence of Autocorrelations in Ultra-High-Frequency Stock Returns

Abstract

Social and economic systems are complex adaptive systems, in which heterogenous agents interact and evolve in a self-organized manner, and macroscopic laws emerge from microscopic properties. To understand the behaviors of complex systems, computational experiments based on physical and mathematical models provide a useful tools. Here, we perform computational experiments using a phenomenological orderdriven model called the modified Mike-Farmer (MMF) to predict the impacts of order flows on the autocorrelations in ultra-high-frequency returns, quantified by Hurst index H r . Three possible determinants embedded in the MMF model are investigated, including the Hurst index H s of order directions, the Hurst index H x and the power-law tail index α x of the relative prices of placed orders. The computational experiments predict that H r is negatively correlated with α x and

Stochastic analysis using public data for forecasting of epidemic spreading of the novel coronavirus disease

“…Due to uncertainly in the official data about the real cases numbers generated by the low number of tests made in the population generates a large randomness in the data and therefore, makes the use of the stochastic analysis greatly adequate to treat the spread of time evolution of the COVID-19. Furthermore, we derive the stochastic differential equation, in Itô calculus, corresponding to nonlinear Fokker-Planck equation derived in framework of the non-additive statistical mechanics, which must also obey to stylized features of the financial market as inverse cubic law [9][10][11][12][13][14][15][16][17] .…”

New approaches in agent-based modeling of complex financial systems

“…More recently, the concept for determining the key parameters of the agent-based models from empirical data instead of setting them artificially was suggested [20]. Similar concept has also been applied to the order-driven models, which were first proposed by Mike and Farmer [46] and improved by Gu and Zhou [47,48,49,50]. In this family of order-driven models, the parameters of order submissions and order cancellations are determined using real order book data.…”

“…In this family of order-driven models, the parameters of order submissions and order cancellations are determined using real order book data. For comparison, the agent-based models focus more on the behaviors of agents [40,41,42,43,44,45], while the order-driven models are mainly intended to explore the dynamics of the order flows [46,47,48,49,50]. In section 2, we review several agent-based models that are based on the agents' behaviors with heterogenous personal preferences and interactions.…”

Ising model of financial markets with many assets

“…Another promising approach is followed by the young family of empirical order-driven models. These models use empirical order-flow data to generate transactions via the continuous double auction mechanism and are able to reproduce statistical price features without freely adjustable parameters in a quantitative way [6,7,8,9,10].…”