Macroscopic Look at Equity Markets

Abstract

Financial markets contribute to the stability of the global economy. A vivid example of this crucial connection is the crash in 2008. Although this connection is well-established, the underlying structure of markets is complex. Complex systems such as this tend to operate in a nonlinear fashion, generating extreme and rare events. In the era of high-frequency trading, we have been witnessing other unusual and extreme phenomena such as flash crashes and technical difficulties due to glitches. Given the presence of these phenomena, a powerful tool is needed to monitor markets' behavior and activities. Recent research in finance has mainly focused on analyzing individual stocks (i.e., microscopic analysis) while ignoring the overall interactions and dynamics between them (i.e., macroscopic analysis), which is crucial to identify abnormalities. To better represent markets' behavior, this dissertation proposes a novel macroscopic perspective, allowing for prediction and understanding of anomalies. Although, the focus of this dissertation is mainly on equity (or stocks) markets, the proposed methods are general such that it can be extended to other financial markets.

In the first part of this dissertation, we propose new sensors to monitor equity markets, adopting a macroscopic perspective. This perspective offers new insights into the physics of stocks. Briefly, we analyze stocks within the context of fluid dynamics in which the movement of stocks is viewed as particles within the “fluid flow” context. For the first time, concepts from physics are utilized and incorporated in modeling both internal and external dynamics. Based on the physics of fluid dynamics, we develop macroscopic variables, such as density, velocity, flux, and pressure. A model consisting of a system of stochastic nonlinear partial differential equations is introduced. The model connects and determines the evolution of macroscopic variables. The validation and usefulness of the new approach is discussed in the last part of this chapter.

The second part extends the analysis to examine the structural properties of the proposed model. We show that the model exhibits weak solutions, such as shock and rarefaction waves. These solutions provide a new narrative about financial shocks. We also present a theoretical analysis of the behavior of the macroscopic variables. To solve the system of stochastic nonlinear partial differential equations adaptively, we devise an integrative algorithm which combines numerical methods and stochastic filtering techniques. This algorithm is tested on abnormal and normal trading days. The results suggest that abnormalities can be identified.

In the third part, we tackle the problem of detecting medium intensity crashes, which are macroscopic abnormalities occurring on a given trading day. These abnormalities create an imbalance with normal market activities because they rarely occur. To address these challenges, we present a cost-sensitive classification model based on a recurrent neural-network called Reservoir Computing (RC). We also extend the classical RC to process predictions from the physics-based model presented in Chapter 2. This approach includes information about the underlying mechanism of the markets, showing significant improvement in detection accuracy.

This dissertation offers a macroscopic perspective by incorporating internal and external dynamics. Market makers can use this perspective to detect irregularities and questionable practices. When market makers are more aware, regular investors will no longer worry that they are trading in a losing or rigged game.