In this dissertation we take a look at the rise of interest rate basis spreads in the market
following the liquidity and credit crunch of 2008. We show that post 2008 the valuation of
all interest rate instruments of a single yield curve for a particular currency is no longer a
feasible approach and the assumption of no arbitrage between di erent tenors is no longer
applicable. Following that a closer look is taken into the cause of such widening basis
spreads and the impact they have had on the market with a focus on reconstituting the
no arbitrage argument and looking at a post crisis multiple curve framework following
an axiomatic approach as introduced by Henrard  and further explored by Bianchetti
and Morini [6, 50]. A bottom-up market approach is taken by Ametrano  and the two
approaches are shown to be equivalent in result. An analogy is made to quanto style cross
currency swap adjustments observed by the aforementioned authors as well as Michaud
and Upper , and Tuckman and Por rio .
We proceed to look at the approaches taken by authors such as Henrard [36, 37] in ex-
tending the Black and Stochastic Alpha Beta Rho models to include basis spreads and
Kijima et al.  who extend a model introduced by Boenkost and Schmidt  and put
forward a quadratic Gaussian model and a Vasicek model. Mercurio  puts forward
an extension to the LIBOR Market Model (also referred to as the Brace-Gatarek-Musiela
model) under both forward measures and spot measures.
Finally we consider the rise of using overnight index swaps in construction OIS discount curves and their application in the valuation of interest rate derivatives in the presence
of collateral as well as reconciling the spread between OIS and vanilla interest rate swaps
with credit risk measures.