This paper establishes a basic framework to study three different variants of Participating Mortgages (PMs). We obtain results for Shared Appreciation Mortgages (SAMs), Shared Income Mortgages (SIMs) and Shared Equity Mortgages (SEMs) in closed-form. We illustrate our findings with examples that show PMs are also attractive in an environment where prepayment can occur. Finally we conclude with the public policy implications of employing PMs as workout loans, especially post sub-prime crisis. We argue that by facilitating better risk sharing, PMs offer a means to enhance the efficiency and resiliency of the financial system.

Risk-neutral and real-world densities are derived from option prices and risk assumptions, and are compared with historical densities obtained from time series. Two parametric risk-transformations are used to convert risk-neutral densities into real-world densities. Both transformations are estimated by maximizing the likelihood of observed index levels, for two parametric density families. Results for the FTSE-100 index show that parametric densities derived from option prices have more explanatory power than historical densities and higher likelihoods than densities estimated by spline methods. A combination of parametric real-world and historical densities provides the preferred predictive densities.