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The hazard rate, also known as the hazard function or failure rate, is a statistical measure used to describe the instantaneous rate at which an event occurs, given that the event has not yet happened. From a probabilistic perspective, it represents the likelihood that a subject will experience the event in a very small time interval, conditional on surviving up to the beginning of that interval. In terms of frequency, the hazard rate can be viewed as the ratio of the number of events to the...

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Updated: Jul 25, 2025

An R-Based Landscape Validation of a Competing Risk Model

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Asset pricing with long-run disaster risk.

Rujie Fan¹, Chao Xiao¹

¹School of Finance, Southwestern University of Finance and Economics, Chengdu, Sichuan, China.

|June 27, 2023

Summary

This study introduces a new disaster model incorporating long-run disaster risk, improving explanations of asset returns compared to traditional models. The findings offer a novel perspective on how disaster risk influences financial markets.

Area of Science:

Economics
Financial Markets
Econometrics

Background:

Traditional disaster models struggle to accurately explain asset returns due to limitations in accounting for time-varying disaster risk.
Existing models do not fully capture the nuances of rare economic disasters and their impact on financial data.

Purpose of the Study:

To develop a novel disaster model that incorporates long-run disaster risk to better match observed asset return moments in U.S. data.
To redefine rare economic disasters and their associated risks within a new theoretical framework.
To identify an additional channel through which disaster risk affects asset returns.

Main Methods:

Redefinition of rare economic disasters.
Development of a novel disaster model featuring long-run disaster risk.

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Modeling the long-run component of consumption growth as a function of time-varying disaster probability.

Empirical validation using U.S. asset return data.

Main Results:

The novel disaster model with long-run disaster risk demonstrates a superior fit to U.S. asset return data compared to traditional models with time-varying disaster risk.
The model successfully matches key asset return moments.
An additional mechanism linking disaster risk to asset returns is uncovered.

Conclusions:

The proposed model offers a more accurate explanation of asset returns by integrating long-run disaster risk.
This research bridges the gap between long-run risk models and rare disaster models in financial economics.
The findings provide new insights into the complex relationship between economic disasters and asset pricing.