A Levy-driven Ornstein-Uhlenbeck process for the valuation of credit index swaptions

TL;DR

This paper introduces a Levy-driven Ornstein-Uhlenbeck model for credit index option valuation, capturing credit market dynamics with gamma processes, and provides analytical formulas, numerical methods, and market calibration results.

Contribution

It develops a novel Levy-driven Ornstein-Uhlenbeck process incorporating gamma processes for credit risk modeling, with explicit formulas and calibration to market data.

Findings

Convergence of numerical methods to analytical solutions

Successful calibration to market prices

Model captures credit spread dynamics effectively

Abstract

A Levy-driven Ornstein-Uhlenbeck process is proposed to model the evolution of the risk-free rate and default intensities for the purpose of evaluating option contracts on a credit index. Time evolution in credit markets is assumed to follow a gamma process in order to reflect the different pace at which credit products are exchanged with respect to that of risk-free debt. Formulas for the characteristic function, zero coupon bonds, moments of the process and its stationary distribution are derived. Numerical experiments showing convergence of standard numerical methods for the valuation PIDE to analytical and Montecarlo solutions are shown. Calibration to market prices of options on a credit index is performed, and model and market implied summary statistics for the underlying credit spreads are estimated and compared.