Paper: arXiv 2503.23992

Abstract

Loss Given Default (LGD) is a key risk parameter in determining a bank’s regulatory capital. During LGD-estimation, realised recovery cash flows are to be discounted at an appropriate rate. Regulatory guidance mandates that this rate should allow for the time value of money, as well as include a risk premium that reflects the “undiversifiable risk” within these recoveries. Having extensively reviewed earlier methods of determining this rate, we propose a new approach that is inspired by the cost of capital approach from the Solvency II regulatory regime. Our method involves estimating a market-consistent price for a portfolio of defaulted loans, from which an associated discount rate may be inferred. We apply this method to mortgage and personal loans data from a large South African bank. The results reveal the main drivers of the discount rate to be the mean and variance of these recoveries, as well as the bank’s cost of capital in excess of the risk-free rate. Our method therefore produces a discount rate that reflects both the undiversifiable risk of recovery recoveries and the time value of money, thereby satisfying regulatory requirements. This work can subsequently enhance the LGD-component within the modelling of both regulatory and economic capital.

Complexity vs Empirical Score

  • Math Complexity: 4.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Street Traders — practical and empirical, lighter on theory

Why this score: The paper employs advanced financial mathematics (e.g., cost of capital models, Solvency II inspiration) but lacks complex stochastic calculus or novel mathematical proofs, focusing on applied financial engineering. It demonstrates strong empirical rigor by applying the method to real bank data from two portfolios, detailing results on drivers like mean and variance, though it does not present full backtest performance metrics or code.

Research Flowchart

  flowchart TD
  A["Research Goal: Determine LGD Discount Rate<br>Reflecting Time Value & Undiversifiable Risk"] --> B["Methodology: Cost of Capital Approach<br>inspired by Solvency II"]
  B --> C["Inputs: Mortgage & Personal Loan Data<br>from South African Bank"]
  C --> D["Process: Estimate Market-Consistent Price<br>for Defaulted Loan Portfolio"]
  D --> E["Computation: Infer Discount Rate<br>from Recovery Mean, Variance & Cost of Capital"]
  E --> F["Outcome: Rate satisfies regulatory requirements<br>Enhances Regulatory & Economic Capital Models"]

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0 of 70 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.