A study on interest rate basis - risk models after the 2008 liquidity crunch

Abstract

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a particular currency is no longer a feasible approach and the assumption of no arbitrage between di erent tenors is no longer applicable.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 [37] and further explored by Bianchetti and Morini [6, 50]. A bottom-up market approach is taken by Ametrano [2] 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 [47], and Tuckman and Por rio [57]. 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. [42] who extend a model introduced by Boenkost and Schmidt [11] and put forward a quadratic Gaussian model and a Vasicek model. Mercurio [46] 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.