ON SAVINGS ACCOUNTS IN SEMIMARTINGALE TERM STRUCTURE MODELS

Abstract

This paper is concerned with term structure models generated by semimartingales in general filtrations. Our main focus is on implied savings accounts for which we provide a simple existence proof and a precise formulation of a uniqueness result previously stated (with an incomplete proof) in a Brownian filtration. We also show that a continuous implied savings account can be replicated by a roll-over strategy in just maturing bonds. Finally, we give a necessary and a sufficient condition for the existence of forward rates and illustrate our results in a number of examples.

Keywords:

• Term structure of interest rates
• Semimartingales
• Super-martingale term structure model
• Multiplicative decomposition
• Implied savings account
• MSC 2000 CLASSIFICATION NUMBERS: 60G48, 91B28, 91B70

ACKNOWLEDGMENTS

We are grateful to Tomas Björk, Marek Musiela and Walter Schachermayer for helpful comments and useful suggestions. Special thanks are due to Christophe Stricker for his help in the preparation of this paper.