This article focuses on the asset price volatility at the stock exchange that result from the regime switching behaviour in the market. This study is devoted to the question about how the asset price volatility affects the US sovereign debt market. The efficient market hypothesis has been a base for the asset pricing. This hypothesis is discussed in this study. The review of the literature reveals nuances of behavioural finance theory, and allows us to better understand the regime switching behaviour in the market. The object of empirical study is the US sovereign debt market. We use the Markov Regime-Switching ARCH (SWARCH) model to analyse data. The results show that there is high volatility regime in both the 2012 and 2017 bonds US market, which significantly affects bond prices. © 2017 The Author(s).