The Gauss+ and LIBOR Market Models
The previous chapters in Part Three are extremely useful for learning about term structure models and for basic applications. Most models used in practice, however, are much more complex. This chapter presents two models that can be and that are used in practice. The first, the Gauss+ model, is a multi-factor generalization of the short-rate models presented in previous chapters. The second, the LIBOR market model (LMM), is in a different family of models: its factors are market observable forward rates.
The mathematical sophistication required to understand and apply this chapter is higher than that required to understand most of the rest of the book. In exchange, however, the reader will understand the key concepts behind many state-of-the-art models, be able to implement the Gauss+ model and a simple version of the LMM model, and certainly be well prepared for further study in this field.
THE GAUSS+ MODEL
The Gauss+ model is well-known among practitioners for use in relative value trading and hedging. The assumptions of the model are intuitively appealing and lead to a reasonable balance between tractability and capturing the empirical complexity of term structure dynamics. The goal of this chapter is to enable a determined reader to implement the model and estimate its parameters. Sample results from the USD and EUR swap markets are provided as well.
The dynamics of the cascade form of the model are given in equations (11.1) through ...