Paper: arXiv 2508.07774

Authors: Quirini Lorenzo, Vannucci Luigi, Quirini Giovanni

Abstract

A model is developed to assess the profitability of loans or mortgages with a specified repayment schedule. Financial institutions face two competing risks: default and prepayment, both influenced by the stochastic evolution of credit market conditions. This study focuses on the Random Net Present Value (RNPV) as a key performance metric. The analysis evaluates the mean and variance of the RNPV at both the individual loan level and the portfolio level, within a unified framework that accounts for borrower behavior and prevailing credit market dynamics.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework modeling loan profitability via Random Net Present Value (RNPV) using a Markov Chain for market states and competing risks for default and prepayment. While the theoretical derivations for the first two moments at the loan and portfolio levels are detailed and clear, the empirical side relies mostly on a stylized numerical illustration rather than extensive historical backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Assess Loan Profitability via RNPV under Prepayment & Default Risks] --> B[Inputs: Repayment Schedules & Stochastic Credit Market Conditions]
    B --> C[Unified Risk Model: Simultaneous Prepayment & Default Hazard Rates]
    C --> D[Computational Engine: Calculate Individual & Portfolio RNPV]
    D --> E[Outcomes: Mean and Variance of RNPV for Individual Loans & Portfolios]

Cited References (14)

  1. Classical Competing Risks (2001)
  2. Multivariate Survival Analysis and Competing Risks (2012)
  3. Competing Risks and Multistate Models with R (2012)
  4. Using Hidden Markov Model to Monitor Possible Loan Defaults in Banks (2020)
  5. Modeling Credit Risk with Hidden Markov Default Intensity (2018)
  6. A Structural Hidden Markov Model for Forecasting Scenario Probabilities for Portfolio Loan Loss Provisions (2022) — link
  7. Creditworthiness Dynamics and Hidden Markov Models (2014)
  8. Credit scoring with macroeconomic variables using survival analysis (2009)
and 6 more
  1. Analysis of default data using hidden Markov models (2005)
  2. Estimation of the allowance for doubtful accounts by Markov chains (1962)
  3. Survival analysis and the credit granting decision (1992)
  4. Monitoring creditworthiness: Markov chains and replication portfolios (2011)
  5. Survival analysis methods for personal loan data (2002)
  6. Hidden Markov Models for Time Series (2009)

0 of 14 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.