Towards a central interest rate model (Q2771109)

There are many interest rate models, but because of the complexity of fixed-income instruments the most widely use by practitioners are those that are mathematically tractable. Basically, these models can be grouped in two classes: the Libor rate models and the swap rate models. The former are suitable for pricing caps while the latter effectively price swaptions. Nevertheless, these two approaches are incompatible and inappropriate for dealing with, for example, cross-markets exotics.NEWLINENEWLINEThe authors intend, and succeed, to show that the Libor model could be the unifying (central) interest rate model capable of including the main properties of the swap rate models and providing a consistent pricing framework for a variety of instruments, in particular pure swap market products.NEWLINENEWLINEConcretely, they consider a discrete lognormal forward Libor rate model and derive pricing formulae for swaps and swaptions within this model. The Black swaption pricing formula, the corresponding sensitivities (the Greeks) and swaption hedging in the swap rate model setting are revisited. Under certain assumptions, that are backed by numerical analysis, the swap rate dynamics and volatility along with the Greeks are approximated in the Libor model. All these approximations are tested numerically on a range of swaptions for two different volatility structures. The results suggest that the approximate equations within the lognormal Libor model for swaptions give values close to the ones of the swap rate models and those observed in the market. Consequently, the Libor model could be used not only for pricing caps but also swaptions and exotics.NEWLINENEWLINEFor the entire collection see [Zbl 0967.91001].