Financial networks are dynamic systems composed of numerous elements, and research using mathematical, physical, and informatics approaches has been growing. For instance, financial crises such as the Lehman shock and the European debt crisis are rooted in the systemic risks of financial networks and the chaos in financial markets caused by the crowd behavior of unsettled market participants. The elucidation of these mechanisms is highly sought after. Thus, while considering both the dynamic and network aspects of financial markets, efforts are being made to elucidate the mechanisms of financial markets using physical and engineering approaches.
(1) Research on Prospect Theory
The impact of human behavioral psychology on economics and finance is well-known through Prospect Theory, proposed by Daniel Kahneman and Amos Tversky. According to this theory, in uncertain environments, humans become risk-takers in the domain of losses and risk-averse in the domain of gains. Thus, it is typical for non-rational psychological factors to influence decision-making, and these factors are expected to be reflected in financial markets as well.
Therefore, by analyzing financial transaction data, research is conducted focusing on non-rational human behavior patterns, such as those characterized by crowd psychology and panic, as represented by Prospect Theory. This involves statistically analyzing the behavioral tendencies of market participants [1].
[1] Y.Y. Liu*, J.C. Nacher*, T. Ochiai*, M. Martino and Y. Altshuler, “Prospect Theory for Online Financial Trading”,
PLoS ONE 9(10): e109458 (2014)
*These authors contributed equally to this work.
[Link to the paper], [PDF]
(2) Research on Deviations from Randomness in Financial Markets
Historically, for financial risk management and other applications, models such as the ARCH and GARCH models have been proposed, where volatility varies over time, as well as models using fractional Brownian motion that can describe market trends. These models have enabled a more accurate description of the market beyond simple geometric Brownian motion modeling.
These traditional models are Markovian, where the current price depends only on the very recent past. However, our research has shown that these Markovian models do not adequately reflect the psychological aspects of market participants. For example, the movement of financial asset prices is psychologically influenced by long-past lows or highs. We have examined the statistical properties of price fluctuations using high-frequency intraday data from the past, especially when prices approach these historical lows or highs. Our findings suggest that the probability of surpassing previous highs (or lows) is smaller than in a random walk (due to resistance effects at these levels), but once these levels are breached, the ensuing volatility is greater than in a random walk (acceleration effect at new highs or lows) [2].
These psychological influences of investors have not been considered in traditional price fluctuation models. Our study aims to develop new models of price fluctuations that go beyond Markovian models, and as an application, to propose more realistic risk management techniques and methods for designing financial derivatives.
[2] J.C. Nacher, T. Ochiai, “Foreign exchange market data analysis reveals statistical features that predict price movement acceleration”,
Physical Review E, 85, 056118, 7 pages (2012)
[Link to the paper]