Search arXivSearch

arXiv · 2406.17308

Improving Realized LGD Approximation: A Novel Framework with XGBoost for Handling Missing Cash-Flow Data

Abstract

The scope for the accurate calculation of the Loss Given Default (LGD) parameter is comprehensive in terms of financial data. In this research, we aim to explore methods for improving the approximation of realized LGD in conditions of limited access to the cash-flow data. We enhance the performance of the method which relies on the differences between exposure values (delta outstanding approach) by employing machine learning (ML) techniques. The research utilizes the data from the mortgage portfolio of one of the European countries and assumes a close resemblance to similar economic contexts. It incorporates non-financial variables and macroeconomic data related to the housing market, improving the accuracy of loss severity approximation. The proposed methodology attempts to mitigate the country-specific (related to the local legal) or portfolio-specific factors in aim to show the general advantage of applying ML techniques, rather than case-specific relation. We developed an XGBoost model that does not rely on cash-flow data yet enhances the accuracy of realized LGD estimation compared to results obtained with the delta outstanding approach. A novel aspect of our work is the detailed exploration of the delta outstanding approach and the methodology for addressing conditions of limited access to cash-flow data through machine learning models.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Zuzanna Kostecka, Robert Ślepaczuk. 2024-06-25. Improving Realized LGD Approximation: A Novel Framework with XGBoost for Handling Missing Cash-Flow Data. https://arxiv.org/abs/2406.17308

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Dynamic reinsurance via martingale transport

We formulate a dynamic reinsurance problem in which the insurer seeks to satisfy prescribed terminal moment or risk-based constraints while minimizing the $L^2$-norm of the ceded risk. As a tool for this analysis, we first use techniques from martingale optimal transport to study the auxiliary problem in which the insurer matches a given terminal distribution of the surplus process. We show that, under suitable assumptions, this auxiliary problem admits a tractable solution analogous to the Bass martingale. We then relax this condition by only requiring certain moment or risk-based constraints.

q-fin.RM

Risk Measures under Paired-Ambiguity: A Deep Learning Reflected BSDE Framework

We study optimal stopping under dynamic risk measures with simultaneous ambiguity in the probability model and the discount rate. We introduce a paired ambiguity framework combining Girsanov model uncertainty with cash subadditive risk evaluation and characterize the stopping value by an upper reflected backward stochastic differential equation (BSDE). We establish structural properties of the resulting stopping operator and study quadratic drivers associated with entropic risk measures, obtaining explicit stopping rules in several benchmark cases. We then develop a deep learning scheme for the reflected quadratic BSDE. The convergence analysis uses discrete reflection and truncation to reduce the quadratic problem to a globally Lipschitz system and combines reflected BSDE discretization estimates with neural network approximation errors. Numerical experiments for American options illustrate the effects of discount rate and entropic ambiguity on stopping values and exercise decisions.

q-fin.RM

When Is the Gini Loading More Prudent? Tail Structure and the Ordering of the Standard Deviation and the Gini Mean Difference

The standard deviation (SD) and the Gini mean difference (GMD) are the two canonical measures of variability used to load premiums, set risk margins and allocate capital, yet no universal ordering between them exists. We show that the comparison is \emph{equivalent} to asking whether the coefficient of variation of the spacing $|X-X'|$ generated by two independent copies of the risk exceeds unity, so that the exponential law -- whose spacing is again exponential -- is the universal knife-edge separating the two regimes. Reading the GMD as twice the maxiance, that is, as a second-order \emph{dual} moment in the sense of Yaari's dual theory, the problem becomes an explicit comparison of primal and dual second-order variability. We derive a closed-form representation of the mean excess function of the spacing in terms of the hazard and reverse hazard rates of $X$, and use it to prove that heavy-tailed behavior -- a decreasing hazard rate or an increasing reverse hazard rate -- yields SD dominance, whereas two-sided light tails yield GMD dominance; within the monotone aging classes, equality characterizes the exponential law. Both regimes are stable under truncation, convolution and mixing, which makes them operational in collective risk and frailty models. We classify the severity, lifetime and frequency distributions of actuarial practice accordingly, quantify the consequences for SD- and Gini-loaded premium principles and for Gini-type tail risk measures, and show that the sign of $\mathrm{SD}-\mathrm{GMD}$ across thresholds furnishes a simple diagnostic for tail aging.

q-fin.RM