This paper investigates the relationship between trading volume and volatility for four international stock markets (US: S&P500, UK: FTSE100, France: CAC40 and Germany: DAX30) in a context of global financial crisis. Unlike previous related studies, we use intraday data and apply a nonlinear econometric model to assess this relationship. In particular, we first break down intraday realized volatility into its continuous and jump components using the non-parametric approach developed by Barndorff-Nielsen and Shephard (J Financ Econom 4:1–30, 2006). Second, we investigate the volume–volatility relationship and test whether it varies according to volatility components (jumps and continuous component). While Giot et al. (J Empir Finance 17:168–175, 2010), among others, investigated the volume–volatility relationship in a linear context, our study contributes by estimating different nonlinear specifications (threshold model, nonlinear Tobit model) that enable us to capture further asymmetry and time-variation to better apprehend the effect of trading volume on realized volatility. Accordingly, our study yields two interesting findings. On the one hand, as expected there is a significant and positive relationship between trading volume and realized volatility, as well as with its components, confirming the importance of trading volume as a key to characterizing volatility. On the other hand, we show that this relationship exhibits asymmetry and nonlinearity, and that threshold models are more appropriate than linear model to characterize the volume volatility relationship.