The new interest rate models. Recent developments in the theory and application of yield curve dynamics (Q2756620)

The mathematical theory of interest rate models continues to be one of the most important areas of modern finance. The articles included in the present volume indicate the many directions in which the subject has developed over the last decade. The book is divided into four sections.NEWLINENEWLINENEWLINEThe first section, called ``Forward Short Rate Models and their Empirical Consequences'', includes the Heath, Jarrow and Morton (1992) paper, one of the most influential papers on interest rates ever published, along with articles by Flesaker (1993), Amin and Morton (1993) and Ritchken and Sankarasubramanian (1995).NEWLINENEWLINENEWLINEThe second section ``Short rate models new and old'', includes well-known works by Chan, Karolyi, Longstaff and Sanders (1992), Carverhill (1994) and Ait-Sahalia (1996), as well as two important new papers by Pearson and Zhou (2000) and by Vasicek (2000).NEWLINENEWLINENEWLINEThe third section of the book is entitled ``Potentials and positive interest''. Here we find a number of articles that, in various ways, develop a line of enquiry originated in the remarkable paper of Constantinides (1992), who introduces the idea of pricing kernels into interest rate theory. The paper of Rogers (1997), which has been very influential as a stimulus to further development in this area, suggests that there may yet be many fruitful ideas already developed by probabilists that can be successfully enlisted in the quest for a better interest rate model. The papers by Rutkowski (1997) and by Flesaker and Hughston (1997c) explore and further develop the ``positive interest'' approach, which ties in very neatly with the potential theories. The paper by Hunt, Kennedy and Pelsser (2000) introduces a class of Markov models that includes nearly all current models of practical importance.NEWLINENEWLINENEWLINEThis paper acts also as a bridge to the final section, ``From Market Models to Hilbert space theories of the term structure'', where the reader will find articles by Sandmann and Sondermann (1993), Duffie and Kan (1996), Kennedy (1996), Björk and Christensen (1999) and by Bouchaud, Sagna, Cont, El-Karoui and Potters (1998). A common theme in a number of the articles in this section is the idea of modelling the yield curve as a dynamical object in its own right. An important theoretical consequence of that line of investigation has been to stimulate further developments in dynamical theories of the yield curve.NEWLINENEWLINENEWLINEIn the Introduction written by Lane P. Hughston, who is also the editor of the volume, a summary of the most basic ideas essential to interest rate modelling is presented. These and related investigations, which bring in powerful new mathematical tools, may form the basis of a truly dynamical theory of interest rates.NEWLINENEWLINENEWLINEThis is a very interesting and important book.