Multiple defaults and contagion risks

TL;DR

This paper develops a comprehensive framework for modeling multiple defaults and contagion risks in financial markets, providing a new pricing formula and an optimal investment approach that accounts for interconnected default events.

Contribution

It introduces a general pricing formula using progressive filtration enlargement and establishes a recursive method for optimal investment in contagion risk scenarios.

Findings

Derived a pricing formula relating enlarged and reference filtrations

Interpreted the formula as a Radon-Nikodym derivative of random measures

Proposed a recursive approach for optimal investment under contagion risks

Abstract

We study multiple defaults where the global market information is modelled as progressive enlargement of filtrations. We shall provide a general pricing formula by establishing a relationship between the enlarged filtration and the reference default-free filtration in the random measure framework. On each default scenario, the formula can be interpreted as a Radon-Nikodym derivative of random measures. The contagion risks are studied in the multi-defaults setting where we consider the optimal investment problem in a contagion risk model and show that the optimization can be effectuated in a recursive manner with respect to the default-free filtration.