BFS 2002

Contributed Talk

Topologically Pseudo-complete System of Bond Price Processes, and Application to the LIBOR Market Model

Takashi Yasuoka

The problem of continuous-time modeling of term structure of interest rates is studied in a new framework, that is a methodological generalization of the HJM framework \cite{HJM}. A LIBOR market model is the most important example of our framework, because it is not completely described within the HJM framework.
The new framework is introduced so as to admit both the LIBOR market model and the HJM model, and it shows that the LIBOR market model is described as a limit of the sequence of the HJM models. In other words, the set of HJM models is topologically dense in our framework.
In particular our results show that the LIBOR market model provides some financial properties similar to those of the Jamshidian model(1997) (cf. Musiela and Rutkowski(1997)).
It is expected that our approach is applicable to construct other financial model which may not stay in the HJM framework, for example, a credit model based on LIBOR.