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Interest Rates and The Credit Crunch: New Formulas and Market Models Fabio Mercurio QFR, Bloomberg_ First version: 12 November 2008 This version: 8 July 2009 Abstract We start by describing the major changes that occurred in the quotes of market rates after the 2007 subprime mortgage crisis. ment on their lost analogies and consistencies, and hint ona possible, simple way to formally reconcile them. We then show how to price interest rate swaps under the new market practice of using different curves for generating future LIBOR rates and for discounting cash flows. Straightforward modifications of the market formulas for caps and swaptions will also be derived. Finally, we will introduce a new LIBOR market model, which will be based on modeling the joint evolution of FRA rates and forward rates belonging to the discount curve. We will start by analyzing the basic lognormal case and then add stochastic volatility. The dynamics of FRA rates under different measures will be obtained and closed form formulas for caplets and swaptions derived in the lognormal and Heston(1993) cases. 1 Introduction Before the credit crunch of 2007, the interest rates quoted in the market showed typical consistencies that we learned on books. We knew that a floating rate bond, where rates are set at the beginning of their application period and paid at the end, is always worth par at inception, irrespe