Perturbation Methods in Credit Derivatives

CHAPTER 14Multi‐Curve Framework

14.1 BACKGROUND

In our discussion hitherto we have based our calculations on the assumption that, for any given currency there is a single yield curve which can be used for the purpose both of calculating discount factors (the discounting curve) and of fixing LIBOR rates (the forward curve). As is well known, this is only true to a first approximation in current markets: since the credit crunch which began in 2007, longer‐term LIBOR rates have been trading at a premium over shorter‐term rates, reflecting the credit risk associated with the term of the loan/investment with which the LIBOR payment is associated. As observed by Mercurio [2010]:

When August 2007 arrived, the market had to face an unprecedented scenario. Interest rates that until then had been almost equivalent, suddenly became unrelated, with the degree of incompatibility that worsened as time passed by. For instance, the forward rate implied by two deposits, the corresponding FRA rate and the forward rate implied by the corresponding OIS rates became substantially different, and started to be quoted with large, non‐negligible spreads.

Consequently, practitioners typically build a “risk‐free” discounting curve from OIS (daily compounded overnight) rates, or swaps based thereon. For each LIBOR tenor for which forward rates need to be produced in the course of a calculation, a separate curve is built with reference to market instruments (swaps, futures and/or forward rate agreements) ...