Pricing approximations and error estimates for local L\'evy-type models with default

TL;DR

This paper develops approximation methods and error bounds for solving complex integro-differential equations in financial models involving defaultable assets with Le9vy-type processes, supported by numerical examples.

Contribution

It introduces new approximation techniques and rigorous error estimates for partial integro-differential equations in default risk modeling with Le9vy processes.

Findings

Derived explicit error bounds for approximations.

Validated methods with numerical examples across financial scenarios.

Enhanced understanding of defaultable asset modeling with Le9vy processes.

Abstract

We find approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar L\'evy-type stochastic processes. We derive rigorous error bounds for the approximate solutions. We also provide numerical examples illustrating the usefulness and versatility of our methods in a variety of financial settings.