LIBOR Models

This research area concentrates on the modeling of the term structure of interest rates and the pricing of interest rate derivatives. The LIBOR market model is favored by practitioners, however has certain well-know pitfalls. The random terms entering the drift are among the most important pitfalls, since exact closed-form pricing formulas cannot be derived and one has to resort to approximations, the “frozen drift” method being the most popular one. In recent work, Papapantoleon, Schoenmakers and Skovmand (2011) consider a LIBOR model driven by a multi-dimensional Lévy process and develop approximations for the dynamics of rates, which can be simulated quickly and provide accurate prices for both vanilla and path-dependent derivatives. In a related line of research, Keller-Ressel, Papapantoleon and Teichmann (2011) have proposed a new approach for modeling LIBOR rates based on affine processes, which circumvents the problems of the LIBOR market model. In this model, the dynamics of rates remain exponentially affine processes under any forward measure, which allows to price options efficiently using Fourier methods. Moreover, closed-form solutions (a là Black-Scholes) have been derived for the Cox-Ingersoll-Ross process. The different approaches are summarized and compared in Papapantoleon (2010).

Selected Publications