### Abstract

In previous works, the author introduced metric spaces of term structure models to study the relation between the LIBOR market model and the HJM model. However that framework is not comprehensive, nor does it admit an extendable structure. This paper introduces a new metric space to better develop the perspective argument. A metric space is naturally constructed on the set of bond price processes such that the space allows many types of term structure models. This metric presents a general view on the relation between the LIBOR market model and the HJM model. Consequently, the LIBOR market model is placed at the boundary of the HJM model set.

Original language | English |
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Pages (from-to) | 11 |

Number of pages | 16 |

Journal | Journal of Math-for-Industry |

Volume | 5 |

Issue number | 2013A-2 |

Publication status | Published - 2013 |

### Keywords

- term structure model
- LIBOR market model
- BGM model
- metric space

### ASJC Scopus subject areas

- Economics, Econometrics and Finance(all)

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## Cite this

Yasuoka, T. (2013). L2-theoretical study of the relation between the LIBOR market model and the HJM model.

*Journal of Math-for-Industry*,*5*(2013A-2), 11. http://j-mi.org/articles/view/281