Smile Pricing and Hedging Caps and Swaptions in Libor Market Model and Its Simple Extension

This paper presents an extensive test of the Libor Market on the Euro Cap and Swaption market. The deterministic LIBOR market model prices OTC cap exactly and prices OTC swaptions with errors well below two basis points. Tests for the hedging performance show that the deterministic LIBOR market model is more effective in hedging in- and at-the money OTC caps and swaptions. The simple extended LIBOR market model under the displaced diffusion dynamics is sufficient to model the Euro caplet smile surface, with pricing errors for caplets across strikes below one basis point. The implied swaption smile for the Euro market takes on a similarly symmetric shape as the cap counterpart