Brownian Bridges on Random Intervals

TL;DR

This paper introduces Brownian bridge processes on random intervals to model market information flow about company defaults, revealing how proximity to zero indicates imminent default risk.

Contribution

It provides the foundational properties of Brownian bridges on stochastic intervals, linking them to financial market default prediction models.

Findings

Bridge process indicates default risk proximity

Process leaks information before default occurs

Captures empirical market behavior

Abstract

The issue of giving an explicit description of the flow of information concerning the time of bankruptcy of a company (or a state) arriving on the market is tackled by defining a bridge process starting from zero and conditioned to be equal to zero when the default occurs. This enables to catch some empirical facts on the behavior of financial markets: when the bridge process is away from zero, investors can be relatively sure that the default will not happen immediately. However, when the information process is close to zero, market agents should be aware of the risk of an imminent default. In this sense the bridge process leaks information concerning the default before it occurs. The objective of this first paper on Brownian bridges on stochastic intervals is to provide the basic properties of these processes.