Cash flow modelling for Residential Mortgage Backed Securities: a survival analysis approach

This thesis describes the research into modelling cash ows for Residential Mortgage Backed Securities (RMBS). RMBS notes are secured by proceeds, interest and principal payments, of the underlying mortgage pool. A transaction is divided into several classes of notes with di�erent risk pro�les, though they all reference to the same underlying assets. The quality or creditworthiness of an RMBS transaction is assessed by credit rating agencies. During the credit crisis substantial losses were su�ered on several RMBS notes, sometimes up to the most senior ones. In response, the rating agencies downgraded a lot of RMBS transactions, and more importantly the market questioned the ability of the rating agencies to assess the quality of structured credits. As a consequence pricing RMBS notes became very subjective. This forces investors to develop their own pricing models instead of relying on rating agencies. Finally, regulatory supervisors have reacted by requesting more transparency from issuers, resulting in the obligation for issuers to make available to investors detailed loan-level data on the underlying mortgage pool. The new regulations gave rise to research on how to purposefully apply loan-level data to consistently and arbitrage free value an RMBS note. In this thesis we develop a model based on loan-level data to forecast the cash ows to the noteholders. This model has a stochastic part, the cash ows from the mortgage pool, and a deterministic part, the allocation of these cash ows to the noteholders established by the transaction structure. Besides interest payments, default and early repayment are determinants of the size and timing of cash ows from the underlying mortgage pool. In this research, both the default and early repayment model are based on survival analysis, which allows for the estimation of month-to-month default and early repayment probabilities at a mortgage level. The Cox proportional hazards model adopted is able to incorporate both mortgage speci�c variables and time-varying covariates relating to the macro-economy. Since both default and early repayment can cause a mortgage to be terminated before maturity, these causes are termed 'competing risks'. In this paper we will extend the Cox model such that it explicitly accounts for the competing risk setting. We �nd that the probability of default for a mortgage is higher if: � the ratio of loan to foreclosure value is higher; � the borrower has a registered negative credit history; � the ratio of main income to total income associated with the loan is higher; � there is only one registered borrower; � the income of the borrower is not disclosed to the lender, but to an intermediary. For early repayment, we �nd that the probability of occurrence for a mortgage is higher if: � the ratio of loan to foreclosure value is higher; � the applicant is younger; � the total income of the borrower(s) is lower; � the 3-months Euribor is higher; � it is an interest reset date; � the re�nancing incentive is higher. We obtain a method to estimate the month-to-month default and early repayment probabilities for a speci�c mortgage with certain characteristics and age. Monte Carlo simulation is used to compute di�erent realisations of default and early repayment for the underlying mortgage pool over the maturity of the RMBS. Finally, the deterministic structure of the notes allows us to derive the corresponding discounted cash ows to the noteholders and estimate a pro�t distribution for an RMBS note. The research resulted in a tool for NIBC to assess the quality of a mortgage pool and employ this information to arbitrage free value a corresponding RMBS note.