Scaling and volatility of breakouts and breakdowns in stock price dynamics

Because the movement of stock prices is not only ubiquitous in financial markets but also crucial for investors, extensive studies have been done to understand the law behind it. In particular, since the financial crisis in 2008, researchers have a more interest in investigating large market volatilities in order to grasp changing market trends.

In this work, we analyze the breakouts and breakdowns of both the Standard & Poor's 500 Index in the US stock market and the Shanghai Composite Index in the Chinese stock market. The breakout usually represents an ongoing upward trend in technical analysis while the breakdown represents an ongoing downward trend. Based on the renormalization method, we introduce two parameters to quantize breakouts and breakdowns, respectively. We discover scaling behavior, characterized by power-law distributions for both the breakouts and breakdowns in the two financial markets with different power-law exponents, which reflect different market volatilities. In detail, the market volatility for breakdowns is usually larger than that for breakouts. Moreover, as an emerging market, the Chinese stock market has larger market volatilities for both the breakouts and breakdowns than the US stock market (a mature market). Further, the short-term volatilities show similar features for both the US stock market and the Chinese stock market. However, the medium-term volatilities in the US stock market are almost symmetrical for the breakouts and breakdowns, whereas those in the Chinese stock market appear to be asymmetrical for the breakouts and breakdowns.

The methodology presented here provides a way to understand scaling and hence volatilities of breakouts and breakdowns in stock price dynamics. Our findings not only reveal the features of market volatilities but also make a comparison between mature and emerging financial markets.