### Abstract

The purpose of this paper is to highlight some of the key elements of the HJM approach as originally introduced in the framework of fixed income market models, to explain how the very same philosophy was implemented in the case of credit portfolio derivatives and to show how it can be extended to and used in the case of equity market models. In each case we show how the HJM approach naturally yields a consistency condition and a no-arbitrage condition in the spirit of the original work of Heath, Jarrow and Morton. Even though the actual computations and the derivation of the drift condition in the case of equity models seems to be new, the paper is intended as a survey of existing results, and as such, it is mostly pedagogical in nature.

Original language | English (US) |
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Title of host publication | Paris-Princeton Lectures on Mathematical Finance 2004 |

Publisher | Springer Verlag |

Pages | 1-50 |

Number of pages | 50 |

ISBN (Print) | 3540733264, 9783540733263 |

DOIs | |

State | Published - Jan 1 2007 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 1919 |

ISSN (Print) | 0075-8434 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Keywords

- Arbitrage-free term structure dynamics
- Health-Jarrow-Morton theory
- Implied volatilty surface
- Local volatility surface
- Market models

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## Cite this

*Paris-Princeton Lectures on Mathematical Finance 2004*(pp. 1-50). (Lecture Notes in Mathematics; Vol. 1919). Springer Verlag. https://doi.org/10.1007/978-3-540-73327-0_1