This pap er intro duces a general framework for market mo dels, namedM arket M o del Approach, through the concept of admissible sets of for-ward swap rates spanning a given tenor structure. We relate this conceptto results in graph theory by showing that a set is admissible if and only ifthe asso ciated graph is a tree. This connection enables us to enumerate alladmissible mo dels for a given tenor structure. Three main classes are iden-ti ed within this framework, and corresp ond to the co-terminal, co-initial,and co-sliding mo del. We prove that the LIBOR market mo del is theonly admissible mo del of a co-sliding typ e. By fo cusing on the co-terminalmo del in a lognormal setting, we develop and compare several approxi-mating analytical formulae for caplets, while swaptions can b e priced bya simple Black-typ e formula. A novel calibration technique is intro ducedto allow simultaneous calibration to caplet and swaption prices. Empiricalcalibration of the co-terminal mo del is shown to b e faster, more robustand more e¢cient than the same pro cedure applied to the LIBOR marketmo del. We then argue that the co-terminal approach is the simplest andmost convenient market mo del for pricing and hedging a large variety ofexotic interest-rate derivatives.
