ボラティリティと市場モデル : 経済物理から経済科学へ(<論文特集>「エコノフィジックス」)  [in Japanese] Volatility and market model : from econophysics to econo-science(<Special Futures>Econophysics)  [in Japanese]

Recent advent of econophysics has been revealing interesting phenomenologies about speculative markets. Specifically, price fluctuations in such markets possess, while serially uncorrelated, long-memory in the magnitude or volatility, quite contrary to what is expected from efficient market hypothesis. The phenomenon is known as volatility clustering, and appears in the time-scales from minutes to months, or even a year. Additional property can be universally observed in the strongly correlated regime as relation between volatilities for different time-scales, or self-similarity. Though such properties have significant and practical implication in financial markets, little is known about the dynamical origin of them. We consider that these properties are manifestation of interdependent agents' aggregate dynamics involving a wide range of time-scales. By using a minimal but interesting model of interacting spins proposed by Bornholdt, we attempt to bridge between market model and phenomenologies concerning volatility by studying the statistical properties of simulation results. It is implied that long-memory and self-similarity are found but in a limited range of time-scales.