A multiple-curve HJM model of interbank risk

In the aftermath of the 2007-2009 nancial crisis, a variety of spreads have developed between quantities that had been essentially the same until then, notably LIBOR-OIS spreads, LIBOR-OIS swap spreads, and basis swap spreads. By the end of 2011, with the sovereign credit crisis, these spreads were again signi cant. In this paper we study the valuation of LIBOR interest rate derivatives in a multiple-curve setup, which accounts for the spreads between a risk-free discount curve and LIBOR curves. Towards this end we resort to a defaultable HJM methodology, in which these spreads are explained by an implied default intensity of the LIBOR contributing banks, possibly in conjunction with an additional liquidity factor. Markovian short rate speci cations are given in the form of an extended CIR and a Lévy Hull White model for a risk-free short rate and a LIBOR short spread. The use of Lévy drivers leads to the more parsimonious speci cation. Numerical values of the FRA spreads and the basis swap spreads computed with the latter largely cover the ranges of values observed even at the peak of the 2007-2009 crisis.