A Defaultable HJM Modelling of the Libor Rate for Pricing Basis Swaps after the Credit Crunch
Final version in the European Journal of Operational Research, Volume 249, Issue 1, 16 February 2016, Pages 238-244 (Forthcoming)
26 Pages Posted: 13 Oct 2015 Last revised: 18 Jan 2016
A great deal of recent literature discusses the major anomalies that have appeared in the interest rate market following the credit crunch in August 2007. There were major consequences with regard to the development of spreads between quantities that had remained the same until then. In particular, we consider the spread that opened up between the Libor rate and the OIS rate, and the consequent empirical evidence that FRA rates can no longer be replicated using Libor spot rates due to the presence of a Basis spread between floating legs of different tenors. We develop a credit risk model for pricing Basis Swaps in a multi-curve setup. The Libor rate is considered here as a risky rate, subject to the credit risk of a generic counterparty whose credit quality is refreshed at each fixing date. A defaultable HJM methodology is used to model the term structure of the credit spread, defined through the implied default intensity of the contributing banks of the Libor corresponding to a chosen tenor. A forward credit spread volatility function depending on the entire credit spread term structure is assumed. In this context, we implement the model and obtain the price of Basis Swaps using a numerical scheme based on the Euler-Maruyama stochastic integral approximation and the Monte Carlo method.
Keywords: Basis swaps, HJM model, Credit crisis, Libor models, Multi-curve term structure modelling
Suggested Citation: Suggested Citation