A Multi Interest Rate Curve Model for Exposure Modelling

Abstract

The tenor basis phenomenon became significant with the 2007 financial crisis and has altered the traditional way of one-curve pricing and risk management to a multi-curve phenomenon. The stochastic nature of basis spreads between curves particularly poses a challenge for forward looking applications like XVA or real world measure exposure analytics. This paper presents a Two- factor Gaussian approach for modelling multiple fixing curves and basis spreads in the risk neutral and spot measure, shows the impact on basis swap exposure, investigates the correlation structure and discusses the pros and cons of interpreting as a spread or multi curve model respectively.

Keywords: exposure modelling, interest rates, stochastic basis, Hull-White, multi factor model

JEL Classification: G12, C63