Asymmetric information in loan contracts: A game-theoretic and statistical approach

Abstract

In this work, we apply game-theoretic and statistical models to examine an open problem regarding asymmetric information in loan contracts. Under these asymmetries, the effect of higher collateral requirements on the interest rates applied by banks to borrowers is not clear. In literature both a positive and a negative link has been backed, based on different hypotheses and econometric analyses. We discuss how this effect cannot be decided a-priori. In the first part we construct three game-theory models under different hypotheses, rigorously proving the theoretical undecidability of an univocal effect. Then, to assess what is the prevailing effect in the reality, we analyze loan big-data for millions of borrowers among various European countries, as collected by the European DataWarehouse. We examine some mathematical and practical aspects of: the Principal Component Analysis (PCA), the Principal Component Regression (PCR), the regularization theory, the LASSO and RIDGE regressions, applying them to our datasets. Finally, we combine a regression model with the Probabilistic PCA, discussing the EM algorithm in presence of sparse datasets. These datasets are characteristic of our database and others, and defining the Probabilistic PCR we propose a new technique which will show itself useful in the hypothesis that the availability of loan data will increase over time conserving some data sparsity.