Counting processes provide a very flexible framework for modeling discrete events that occur over time. Estimation and interpretation are easy, and links to more familiar approaches are at hand. The key is to think of data as "event history", a record of times of switching between states in a discrete state space. In a simple case, the states could be default/nondefault. In other models relevant to credit modeling, the states could be credit scores or payment statuses (30 days past due (dpd), 60 dpd, etc). Here, we focus on the use of stochastic counting processes for mortgage default modeling, using data on high loan-to-value mortgages. Borrowers seeking to finance more than 80% of a house's value with a mortgage usually either purchase mortgage insurance (MI), allowing a first mortgage greater than 80% from many lenders, or use second mortgages. Are there differences in performance between loans financed by these different methods? We address this question in the counting process framework. In fact, MI is associated with lower default rates for both fixed- and adjustable-rate first mortgages.