The eruption of the financial crisis in 2008 caused immense widening of both domestic and cross currency basis spreads. Also, as a majority of all fixed income contracts are now collateralized the funding cost of a financial institution may deviate substantially from the domestic Libor. In this thesis, a framework for pricing of collateralized interest rate derivatives that accounts for the existence of non-negligible basis spreads is implemented. It is found that losses corresponding to several percent of the outstanding notional may arise as a consequence of not adapting to the new market conditions. / I samband med utbrottet av 2008 års finansiella kris vidgades många basisspreadar till ej tidigare skådade nivåer. Därtill krävs i dagsläget att säkerhet finns tillgänglig vid initieringen av en majoritet av alla räntekontrakt, vilket innebär att en banks finansieringskostnad kan avvika substantiellt från den inhemska interbankräntan. I detta examensarbete implementeras ett ramverk för prissättning av räntederivat som beaktar existensen av basisspreadar samt krav på säkerhet. Resultaten visar att förluster motsvarande flera procent av det nominella beloppet kan uppstå som konsekvens av att inte anpassa sig till det nya tillståndet på räntemarknaden.

In this study we analyse relationship between classical approach to valuation of linear interest rate derivatives and post-crisis approach when the valuation better reflects credit and liquidity risk and economic costs of the transaction on top of the risk-free rate. We discuss the method of collateralization to diminish counterparty credit risk, its impact on derivatives pricing, and how overnight indexed swap (OIS) rates became market standard for discounting future derivatives' cash flows. We show that using one yield curve to both estimating the forward rates and discounting the expected future cash flows is no longer possible in arbitrage free market. We review in detail three fundamental interest rate derivatives (interest rate swap, basis swap and cross-currency swap) and we derive discount factors used for calculating the present value of expected future cash flows that are consistent with market quotes. We also investigate drivers behind basis spreads, in particular, credit and liquidity risk, and supply and demand forces, and show how they impact valuation of derivatives. We analyse Czech swap rates and propose an estimation of CZK OIS curve and approximate discount rates in case of cross-currency swaps. Finally, we discuss inflation markets and consistent valuation of inflation swaps.