Hedging of defaultable claims in a structural model using a locally risk-minimizing approach

TL;DR

This paper develops a locally risk-minimizing hedging approach for defaultable claims within a structural model where the underlying is a finite variation Levy process, accounting for jumps and default events.

Contribution

It introduces a novel method for hedging defaultable claims using a locally risk-minimizing approach in a Levy process framework with jumps and default risk.

Findings

Derived explicit Follmer-Schweizer decompositions for defaultable claims.

Extended the locally risk-minimizing approach to non-risk-neutral measures.

Analyzed the impact of jumps on hedging strategies.

Abstract

In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Follmer-Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation Levy process and the claims pay a predetermined payout at maturity, contingent on no prior default. More precisely, in this particular framework, the locally risk-minimizing approach is carried out when the underlying process has jumps, the derivative is linked to a default event, and the probability measure is not necessarily risk-neutral.