Default and prepayment modelling in participating mortgages

Since the 2008 financial crisis, the mortgage market has been renovating its tools and instruments in order to avoid a new crisis. One such innovative instrument is the participating mortgage, in which the lender gains part of the net operating income and/or future appreciation. In this paper, we establish a financing model for participating mortgages, incorporating early termination options such as default and two prepayment clauses, defeasance and prepayment penalty. Later, we illustrate a detailed sensitivity analysis of the model. The values of early termination options depend on the choice of parameters in the model, as well as the term structure of short term rates. Finally, we show that a participation rate of 11.24% results in zero mortgage interest rate using the parameters in our simulation.