| Summary: | The financial markets have changed radically since the start of the 2007 credit crisis. Following the bankruptcies of large financial institutions as well as bailouts of multiple banks and asset management institutions like Bear Sterns, Lehman Brothers, and AIG, the market participants recognised the serious credit and liquidity risks present in the widely traded interest rate derivatives. The effect of rising credit and liquidity risks was observed by the spike in the spreads between nearly risk-free OIS rates used for collateral and risky unsecured LIBOR loan rates. Most of the classical interest rate models used by mentioned market participants relied on the assumption that there exists a risk-free and unique LIBOR lending rate, which is no longer true. This has opened new ground for complex, hybrid models for interest rate derivatives. This PhD thesis presents my work on developing novel interest rate models which are mathematically and historically sound and can be used for pricing interest rate derivatives including stochastic basis spreads between unsecured LIBOR and OIS rates. This work is split into two problems: first we analyse the discrepancies between forward-LIBOR lending rates and their classic replication strategy with spot-LIBOR rates. For this problem, we propose an extension of a known LIBOR Panel Model, which enables us to jointly model OIS and spot- and forward-LIBOR rates with an error within the quoted bid-ask spreads. The second part of this thesis looks into the problem of pricing non-linear derivatives like caps linked to rates on multiple LIBOR tenors. We propose a novel hybrid credit-interest rate model, which allows to jointly model OIS and multi-tenor LIBOR rates and to price multi-tenor caps. The proposed hybrid short-rate model is intuitive, semi-analytically tractable and can be calibrated using liquid, available market data. We compare the market data fit with a benchmark model using fixed LIBOR-OIS spread assumption. The last chapter shows the impact of this model on credit value adjustments for interest rate trades.
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