We propose a class of two factor dynamic models for duration data and related risk analysis in finance and insurance. Empirical findings suggest that the conditional mean and (under) overdispersion of times elapsed between stock trades feature various patterns of temporal dependence. Therefore durations seem to be driven jointly by movements of two underlying factors. The paper presents a new model, called the stochastic volatility duration (SVD) model for processes that involve time varying uncertainty and time related risk. SVD-based estimation of market activity allows for the presence or absence of temporal interactions between the factors, depending on the market organization and the traded stock. The paper presents the distributional properties of SVD, and compares its performance to the performance of ACD models in an empirical study of intertrade durations of the Alcatel stock. Several new diagnostic tools for risk analysis are proposed, such as the conditional overdispersion and Time at Risk.