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Fabio Mercurio


Fabio Mercurio, SSRN, Interest Rates and the Credit Crunch: New Formulas and Market Models, here.  Marco will know where the academic literature has ended up on vanilla swaps and swap futures and probably has a reasonable idea what the various broker dealer IR desks have implemented in production. R. Cont is the other guy, but I never met him.


We start by describing the major changes that occurred in the quotes of market rates after the 2007 subprime mortgage crisis. We comment on their lost analogies and consistencies, and hint on a 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.

Alternative, and more recent, formulations of multi-curve LIBOR market models can be downloaded at:


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