### Abstract

In this paper we model the forward rate process as a stochastic partial differential equation in a Sobolev space. We establish the existence of a martingale measure. We also derive the price of a general contigent claim as the solution to a partial differential equation in an appropriate Hilbert space. Moreover we obtain an explicit formula for the price of the interest rate cap in the Gaussian framework.

Original language | English |
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Title of host publication | Mathematical Finance |

Subtitle of host publication | Workshop of the Mathematical Finance Research Project, Konstanz, Germany, October 5–7, 2000 |

Editors | Michael Kohlmann, Shanjian Tang |

Place of Publication | Basel |

Publisher | Birkhäuser |

Pages | 59-68 |

Number of pages | 10 |

ISBN (Electronic) | 978-3-0348-8291-0 |

ISBN (Print) | 978-3-0348-9506-4 |

DOIs | |

Publication status | Published - 2001 |

Event | Workshop of the Mathematical Finance Research Project 2000 - Konstanz, Germany Duration: 5 Oct 2000 → 7 Oct 2000 |

### Publication series

Name | Trends in Mathematics |
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Publisher | Birkhäuser |

### Workshop

Workshop | Workshop of the Mathematical Finance Research Project 2000 |
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Country | Germany |

City | Konstanz |

Period | 5/10/00 → 7/10/00 |

### Keywords

- Interest rate
- Forward rate
- Martingale measure
- Stochastic partial differential equations
- Gaussian random field

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## Cite this

Bagchi, A., & Suresh Kumar, K. (2001). An infinite factor model for the interest rate derivatives. In M. Kohlmann, & S. Tang (Eds.),

*Mathematical Finance: Workshop of the Mathematical Finance Research Project, Konstanz, Germany, October 5–7, 2000*(pp. 59-68). (Trends in Mathematics). Basel: Birkhäuser. https://doi.org/10.1007/978-3-0348-8291-0_5