Can a Loan Valuation Adjustment (LVA) Approach Immunize Collateralized Debt from Defaults?

This study focuses on structuring tangible asset backed loans to inhibit their endemic option to default. We adapt the pragmatic approach of a margin loan in the configuring of collateralized debt to yield a quasi‐default‐free facility. We link our practical method to the current Basel III (2017) regulatory framework. Our new concept of the Loan Valuation Adjustment (LVA) and novel method to minimize the LVA converts the risky loan into a quasi risk‐free loan and achieves value maximization for the lending financial institution. As a result, entrepreneurial activities are promoted and economic growth invigorated. Information asymmetry, costly bailouts and resulting financial fragility are reduced while depositors are endowed with a safety net equivalent to deposit insurance but without the associated moral hazard between risk‐averse lenders and borrowers

The Bivariate Normal Copula

We collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we provide improved bounds and approximations on the diagonal.Comment: 24 page

Moody's Correlated Binomial Default Distributions for Inhomogeneous Portfolios

This paper generalizes Moody's correlated binomial default distribution for homogeneous (exchangeable) credit portfolio, which is introduced by Witt, to the case of inhomogeneous portfolios. As inhomogeneous portfolios, we consider two cases. In the first case, we treat a portfolio whose assets have uniform default correlation and non-uniform default probabilities. We obtain the default probability distribution and study the effect of the inhomogeneity on it. The second case corresponds to a portfolio with inhomogeneous default correlation. Assets are categorized in several different sectors and the inter-sector and intra-sector correlations are not the same. We construct the joint default probabilities and obtain the default probability distribution. We show that as the number of assets in each sector decreases, inter-sector correlation becomes more important than intra-sector correlation. We study the maximum values of the inter-sector default correlation. Our generalization method can be applied to any correlated binomial default distribution model which has explicit relations to the conditional default probabilities or conditional default correlations, e.g. Credit Risk${}^{+}$, implied default distributions. We also compare some popular CDO pricing models from the viewpoint of the range of the implied tranche correlation.Comment: 29 pages, 17 figures and 1 tabl

Least Dependent Component Analysis Based on Mutual Information

We propose to use precise estimators of mutual information (MI) to find least dependent components in a linearly mixed signal. On the one hand this seems to lead to better blind source separation than with any other presently available algorithm. On the other hand it has the advantage, compared to other implementations of `independent' component analysis (ICA) some of which are based on crude approximations for MI, that the numerical values of the MI can be used for: (i) estimating residual dependencies between the output components; (ii) estimating the reliability of the output, by comparing the pairwise MIs with those of re-mixed components; (iii) clustering the output according to the residual interdependencies. For the MI estimator we use a recently proposed k-nearest neighbor based algorithm. For time sequences we combine this with delay embedding, in order to take into account non-trivial time correlations. After several tests with artificial data, we apply the resulting MILCA (Mutual Information based Least dependent Component Analysis) algorithm to a real-world dataset, the ECG of a pregnant woman. The software implementation of the MILCA algorithm is freely available at http://www.fz-juelich.de/nic/cs/softwareComment: 18 pages, 20 figures, Phys. Rev. E (in press

Estimating Mutual Information

We present two classes of improved estimators for mutual information $M(X,Y)$, from samples of random points distributed according to some joint probability density $\mu(x,y)$. In contrast to conventional estimators based on binnings, they are based on entropy estimates from $k$-nearest neighbour distances. This means that they are data efficient (with $k=1$ we resolve structures down to the smallest possible scales), adaptive (the resolution is higher where data are more numerous), and have minimal bias. Indeed, the bias of the underlying entropy estimates is mainly due to non-uniformity of the density at the smallest resolved scale, giving typically systematic errors which scale as functions of $k/N$ for $N$ points. Numerically, we find that both families become {\it exact} for independent distributions, i.e. the estimator $\hat M(X,Y)$ vanishes (up to statistical fluctuations) if $\mu(x,y) = \mu(x) \mu(y)$. This holds for all tested marginal distributions and for all dimensions of $x$ and $y$. In addition, we give estimators for redundancies between more than 2 random variables. We compare our algorithms in detail with existing algorithms. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis (ICA), for improving ICA, and for estimating the reliability of blind source separation.Comment: 16 pages, including 18 figure

A joint scoring model for peer-to-peer and traditional lending:A bivariate model with copula dependence

We analyse the dependence between defaults in peer-to-peer lending and credit bureaus. To achieve this, we propose a new flexible bivariate regression model that is suitable for binary imbalanced samples. We use different copula functions to model the dependence structure between defaults in the two credit markets. We implement the model in the R package BivGEV and we explore the empirical properties of the proposed fitting procedure by a Monte Carlo study. The application of this proposal to a comprehensive data set provided by Lending Club shows a significant level of dependence between the defaults in peer-to-peer and credit bureaus. Finally, we find that our model outperforms the bivariate probit and univariate logit models in predicting peer-to-peer default, in estimating the value at risk and the expected shortfall

Estimating LGD Correlation

The paper proposes a new method to estimate correlation of account level Basle II Loss Given Default (LGD). The correlation determines the probability distribution of portfolio level LGD in the context of a copula model which is used to stress the LGD parameter as well as to estimate the LGD discount rate and other parameters. Given historical LGD observations we apply the maximum likelihood method to estimate the best correlation parameter. The method is applied and analyzed on a real large data set of unsecured retail account level LGDs and the corresponding monthly series of the average LGDs. The correlation estimate comes relatively close to the PD regulatory correlation. It is also tested for stability using the bootstrapping method and used in an efficient formula to estimate ex ante one-year stressed LGD, i.e. one-year LGD quantiles on any reasonable probability level