# Essays on Modeling and Analysis of Mortgage Loan Pools and the Delphi Method in Forecasting of Financial Variables

Peter Palmroos

Research output: ThesisDoctoral ThesisCollection of Articles

## Abstract

This thesis studies censored and truncated distributions in the modeling of correlation between Probability-of-Default (PD) and Loss Given Default (LGD) in mortgage loan pools, and also the use of the Delphi method in economical and financial forecasting. The first article derives the closed form solution for the moments and correlation of the bivariate, once or twice truncated and/or censored log-normal distribution. As a generalization the formula can also be used for distributions where one or both tails have been partly censored and partly truncated. The central scientific contribution of this paper is the closed form equa-tions for correlation and moments. The model presented in the second article allows the estimation of the heterogeneous mortgage loan pool structure using only the publicly available data. As a result the model gives three matrices of homogenised loan cohorts. Two of these matrices include information on the number of loans and the total remaining principals for all cohorts. The third matrix includes the Current Loan-to-Values (CLTV) for the same cohorts. These CLTVs can be converted to expected LGDs. The presented model is dynamic and can be used for forecasting the future pool structures. The scientific contribution of the paper is the method that can be used to generate reliable estimates of pool structures, when only publicly available data can be used. The third article studies the effects of a mortgage loan pool structure on the observed correlation between PD and LGD. The paper applies the same methods and models presented in the first two essays. Both homogeneous and heterogeneous pool structures are studied. Furthermore, the paper analyses the effects of both including and excluding zero-loss-defaults has on the observed sample correlation. The scientific contribution of the paper is to prove that the observed sample correlations are sometimes so biased that they shouldn't be used as such. In the fourth article forecasting power of the two expert opinion models, Delphi and Face-to-Face meetings, has been tested. We also present two post-survey methods to correct for possible forecast errors. The first model adjusts the perseverance bias caused by overly strong self-confidence of expert panellists, and experts willingness to prefer the trustworthiness of their own estimates over the estimates of other panellists. The second method tests post-survey adjustment of forecasts using conditionalised forecasts. In theory the latter method can be used to increase the accuracy of forecasts when the forecasted variable is dependent on the explanatory variable whose development is hard to forecast. The key scientific contributions of the paper are the support found for the existence of perseverance bias, and the indication that the mechanical post survey corrections of forecasts are possible.
Translated title of the contribution Esseitä asuntoluottosalkkujen mallintamisesta ja analysoinnista sekä Delfoi -menetelmästä taloudellisia muuttujia ennustettaessa English Doctor's degree Aalto University Kuosmanen, Timo, Supervising ProfessorVilmunen, Jouko, Thesis Advisor Aalto University 978-952-60-7108-4 978-952-60-7107-7 Published - 2016 G5 Doctoral dissertation (article)

## Keywords

• Truncated and censored distributions
• Closed-form solution
• Mortgage pool structure
• Correlation between PD and LGD
• Delphi method

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