Defaultable Bonds via HKA

TL;DR

This paper introduces a novel approach using the heat kernel method with Markov process killing to model defaultable bonds, providing explicit formulas and demonstrating practical realism through simulations.

Contribution

It develops a no-arbitrage defaultable bond market model using heat kernel approach with explicit formulas under quadratic Gaussian settings.

Findings

Explicit defaultable bond and credit spread formulas

Model is tractable and aligns with realistic market behavior

Simulation results validate the model's practical applicability

Abstract

To construct a no-arbitrage defaultable bond market, we work on the state price density framework. Using the heat kernel approach (HKA for short) with the killing of a Markov process, we construct a single defaultable bond market that enables an explicit expression of a defaultable bond and credit spread under quadratic Gaussian settings. Some simulation results show that the model is not only tractable but realistic.