Discrete tenor models for credit risky portfolios driven by time-inhomogeneous L\'evy processes

TL;DR

This paper develops a new discrete tenor credit risk model driven by time-inhomogeneous Lévy processes, providing explicit formulas, arbitrage conditions, and a successful calibration to market data.

Contribution

It introduces a novel framework for discrete tenor credit models with Lévy processes, including arbitrage-free conditions, explicit examples, and calibration techniques.

Findings

Model fits iTraxx data well across multiple tranches and maturities.

Provides explicit pricing formulas for STCDOs and options.

Ensures no arbitrage in the proposed dynamic models.

Abstract

The goal of this paper is to specify dynamic term structure models with discrete tenor structure for credit portfolios in a top-down setting driven by time-inhomogeneous L\'evy processes. We provide a new framework, conditions for absence of arbitrage, explicit examples, an affine setup which includes contagion and pricing formulas for STCDOs and options on STCDOs. A calibration to iTraxx data with an extended Kalman filter shows an excellent fit over the full observation period. The calibration is done on a set of CDO tranche spreads ranging across six tranches and three maturities.