American Step-Up and Step-Down Default Swaps under Levy Models

TL;DR

This paper develops a Levy process-based model for valuing flexible default swaps with embedded options, deriving optimal exercise strategies and analyzing how default risk and contract features influence credit spreads.

Contribution

It introduces a novel Levy process framework for pricing step-up and step-down default swaps with optimal stopping analysis, enhancing understanding of their valuation and exercise strategies.

Findings

Derived explicit optimal exercise strategies under spectrally negative Levy models.

Provided numerical analysis of how default risk affects credit spreads.

Demonstrated the impact of contractual features on exercise timing and valuation.

Abstract

This paper studies the valuation of a class of default swaps with the embedded option to switch to a different premium and notional principal anytime prior to a credit event. These are early exercisable contracts that give the protection buyer or seller the right to step-up, step-down, or cancel the swap position. The pricing problem is formulated under a structural credit risk model based on Levy processes. This leads to the analytic and numerical studies of several optimal stopping problems subject to early termination due to default. In a general spectrally negative Levy model, we rigorously derive the optimal exercise strategy. This allows for instant computation of the credit spread under various specifications. Numerical examples are provided to examine the impacts of default risk and contractual features on the credit spread and exercise strategy.