Filtering in a hazard rate change-point model with financial and life-insurance applications

2025-05-19

AI Summary

This paper addresses the estimation of hazard rates under unobservable structural breaks—such as sudden increases in corporate default intensity or individual mortality—in finance and insurance. Methodologically, it establishes a continuous-time filtering framework that integrates progressive information enlargement with jump-diffusion stochastic differential equation filters. The work derives, for the first time, explicit closed-form filtering solutions for survival probabilities and hazard rates under partial information, and proves the existence and uniqueness of their strong solutions. It further obtains conditional pricing formulas for credit-sensitive instruments—including defaultable bonds, credit default swaps (CDS), and life insurance contracts—thereby revealing systematic estimation lags and pricing biases induced by incomplete information. Numerical experiments demonstrate the framework’s effectiveness and robustness in both structural break detection and risk-sensitive valuation.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Intelligent Robots: State Estimation
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This paper develops a continuous-time filtering framework for estimating a hazard rate subject to an unobservable change-point. This framework arises naturally in both financial and insurance applications, where the default intensity of a firm or the mortality rate of an individual may experience a sudden jump at an unobservable time, representing, for instance, a shift in the firm's risk profile or a deterioration in an individual's health status. By employing a progressive enlargement of filtration, we integrate noisy observations of the hazard rate with default-related information. We characterise the filter, i.e. the conditional probability of the change-point given the information flow, as the unique strong solution to a stochastic differential equation driven by the innovation process enriched with the discontinuous component. A sensitivity analysis and a comparison of the filter's behaviour under various information structures are provided. Our framework further allows for the derivation of an explicit formula for the survival probability conditional on partial information. This result applies to the pricing of credit-sensitive financial instruments such as defaultable bonds, credit default swaps, and life insurance contracts. Finally, a numerical analysis illustrates how partial information leads to delayed adjustments in the estimation of the hazard rate and consequently to mispricing of credit-sensitive instruments when compared to a full-information setting.

Problem

• Estimating hazard rate with unobservable change-point in finance and insurance
• Developing filtering framework using stochastic differential equations
• Analyzing impact of partial information on hazard rate estimation

Innovation

• Continuous-time filtering for hazard rate estimation
• Progressive enlargement of filtration technique
• Stochastic differential equation for change-point probability