### Abstract

Interest rate market models, such as the LIBOR market model, have the advantage that the basic model quantities are directly observable in financial markets. Inflation market models extend this approach to inflation markets, where two types of swaps, zero-coupon and year-on-year inflation-indexed swaps, are the basic observable products. For inflation market models considered so far, closed formulas exist for only one type of swap, but not for both. The model in this paper uses affine processes in such a way that prices for both types of swaps can be calculated explicitly. Furthermore, call and put options on both types of swap rates can be calculated using one-dimensional Fourier inversion formulas. Using the derived formulas, we present an example calibration to market data.

Language | English |
---|---|

Pages | 281-301 |

Number of pages | 21 |

Journal | Applied Mathematical Finance |

Volume | 24 |

Issue number | 4 |

DOIs | |

Status | Published - 4 Jul 2017 |

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### Keywords

- affine processes
- inflation options
- Market models

### ASJC Scopus subject areas

- Finance
- Applied Mathematics

### Cite this

*Applied Mathematical Finance*,

*24*(4), 281-301. DOI: 10.1080/1350486X.2017.1378582

**The affine inflation market models.** / Waldenberger, Stefan.

Research output: Contribution to journal › Article

*Applied Mathematical Finance*, vol 24, no. 4, pp. 281-301. DOI: 10.1080/1350486X.2017.1378582

}

TY - JOUR

T1 - The affine inflation market models

AU - Waldenberger,Stefan

PY - 2017/7/4

Y1 - 2017/7/4

N2 - Interest rate market models, such as the LIBOR market model, have the advantage that the basic model quantities are directly observable in financial markets. Inflation market models extend this approach to inflation markets, where two types of swaps, zero-coupon and year-on-year inflation-indexed swaps, are the basic observable products. For inflation market models considered so far, closed formulas exist for only one type of swap, but not for both. The model in this paper uses affine processes in such a way that prices for both types of swaps can be calculated explicitly. Furthermore, call and put options on both types of swap rates can be calculated using one-dimensional Fourier inversion formulas. Using the derived formulas, we present an example calibration to market data.

AB - Interest rate market models, such as the LIBOR market model, have the advantage that the basic model quantities are directly observable in financial markets. Inflation market models extend this approach to inflation markets, where two types of swaps, zero-coupon and year-on-year inflation-indexed swaps, are the basic observable products. For inflation market models considered so far, closed formulas exist for only one type of swap, but not for both. The model in this paper uses affine processes in such a way that prices for both types of swaps can be calculated explicitly. Furthermore, call and put options on both types of swap rates can be calculated using one-dimensional Fourier inversion formulas. Using the derived formulas, we present an example calibration to market data.

KW - affine processes

KW - inflation options

KW - Market models

UR - http://www.scopus.com/inward/record.url?scp=85030554512&partnerID=8YFLogxK

U2 - 10.1080/1350486X.2017.1378582

DO - 10.1080/1350486X.2017.1378582

M3 - Article

VL - 24

SP - 281

EP - 301

JO - Applied mathematical finance

T2 - Applied mathematical finance

JF - Applied mathematical finance

SN - 1350-486X

IS - 4

ER -