外国為替市場の価格変動に対する非マルコフ的な統計的特徴について

抄録

In recent years, several stylized facts have been uncovered in econophysics. Here, we perform an extensive analysis of forex data that leads to unveil a statistical ?nancial law. First, our ?ndings show that, in average, volatility increases more when the price exceeds the highest (lowest) value (i.e. breaks resistance line). We call it (breaking-acceleration e?ect). Secondly, our results show that the probability P(T) to break the resistance line in the past T time follows power-law in both real data and theoretically simulated data. However, the probability calculated using real data is rather lower than the one obtained using a traditional Black-Scholes (BS) model. Taken together, the present analysis characterizes a new stylized fact of ?nancial markets and shows that the market exceeds a past (historical) extreme price fewer times than expected by the BS model (resistance e?ect). However, when the market does it, we predict that the average volatility at that time point will be much higher. These ?ndings indicate that any markovian model does not faithfully capture the market dynamics.