A wave of defaults by US homeowners with tarnished credit histories cascaded through the global financial markets in 2007 and 2008. Mortgage lenders "imploded," hedge funds were forced to close their doors, investment banks collapsed under the weight of subprime mortgage-related losses, a leading insurer was driven to the brink of bankruptcy, and government sponsored mortgage giants Fannie Mae and Freddie Mac were seized by regulators.
Forced to write down three quarters of a trillion dollars in securities backed by subprime mortgages, and with further writedowns likely, financial institutions around the world became far more cautious in their lending, sparking a global credit crisis unparalleled since the Great Depression. Hundreds of lawsuits have been filed, with almost every participant in the subprime mortgage origination and securitization process a potential target.
Biomass can be used as a renewable (green or CO2 neutral) energy source, locally and readily available in large parts of the world. Many studies have been carried out that quantify the potential of the world to produce bioenergy (e.g. (Leemans et al. 1996; Fischer et al. 2001a; Hoogwijk et al. 2004; Smeets et al. 2004a, b). Results indicate that various world regions are in theory capable of producing significant amounts of bioenergy crops without endangering food supply or further deforestation.
A prerequisite for the large-scale production and trade of biomass (biotrade) is that production and trade is beneficial with respect to the social well being of the people (people), the ecosystem (planet) and the economy (profit).
While there is widespread agreement that the value of a mortgage contract subject to prepayment but not default risk should be given by an expectation of the present value of the cash flow, the devil is in the details. A wide variety of approaches have been considered, most of which are commonly classified into one of two categories. One kind of approach has been variously called a reduced form approach, an exogenous approach, an empirical approach, and an econometric approach. The basic idea is to build a stochastic model for interest rates and possibly other economic factors, and then add a statistical model describing how the mortgagor’s prepayment behavior depends on the factors. While such an overall model can be quite complicated, it is usually straightforward to use Monte Carlo simulation to estimate the expected value of the discounted cash flow. Some of the many papers in this category are by Schwartz and Torous [17], [18], Deng [1], Deng, Quigley, and Van Order [2], Gorovoi and Linetsky [7], Kariya and Kobayashi [9], Kariya, Pliska, and Ushiyama [10], and Kau, Keenan, and Smurov [11].
Of significance is that in some of this research, dating back at least to Schwartz and Torous [17], [18], it was recognized that the random time when a mortgagor prepays can be described with a hazard rate model, that is, the conditional rate of prepayment given the current state of any factors and no prepayment to date. Perhaps this development was inspired by the engineering literature on reliability theory, as the time of mortgage prepayment is clearly analogous to the failure time of a system. In any event, Schwartz and Torous [17] used this hazard rate viewpoint in conjunction with a two-factor model in order to present a partial differential equation for the value of a mortgage contract. Moreover, as will be seen in this paper, recent developments involving the hazard rate as a model of a default time in the credit risk literature lead to new results, involving intensity processes, for mortgage contract valuation.
