Increasingly accessible financial data allow researchers to infer market-dynamics-based laws and to propose models that are able to reproduce them. In recent years, several stylized facts have been uncovered. Here we perform an extensive analysis of foreign exchange data that leads to the unveiling of a statistical financial law. First, our findings show that, on average, volatility increases more when the price exceeds the highest (or lowest) value, i.e., breaks the resistance line. We call this the breaking-acceleration effect. Second, our results show that the probability $P\left(T\right)$ to break the resistance line in the past time $T$ 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 different stylized fact of financial markets and shows that the market exceeds a past (historical) extreme price fewer times than expected by the BS model (the resistance effect). However, when the market does, we predict that the average volatility at that time point will be much higher. These findings indicate that any Markovian model does not faithfully capture the market dynamics.

• Received 23 February 2012

DOI:https://doi.org/10.1103/PhysRevE.85.056118