### Abstract

Practitioners are used to value a broad class of exotic interest rate derivatives simply by preforming for what is known as convexity adjustments (or convexity corrections). We start by exploiting the relations between various interest rate models and their connections to measure changes. As a result we classify convexity adjustments into forward adjustments and swaps adjustments.

We, then, focus on affine term structure (ATS) models and, in this context, conjecture convexity adjustments should be related of affine functionals. In the case of forward adjustments, we show how to obtain exact formulas. Concretely for LIBOR in arrears (LIA) contracts, we derive the system of Riccatti ODE-s one needs to compute to obtain the exact adjustment. Based upon the ideas of Schrager and Pelsser (2006) we are also able to derive general swap adjustments useful, in particular, when dealing with constant maturity swaps (CMS).

We, then, focus on affine term structure (ATS) models and, in this context, conjecture convexity adjustments should be related of affine functionals. In the case of forward adjustments, we show how to obtain exact formulas. Concretely for LIBOR in arrears (LIA) contracts, we derive the system of Riccatti ODE-s one needs to compute to obtain the exact adjustment. Based upon the ideas of Schrager and Pelsser (2006) we are also able to derive general swap adjustments useful, in particular, when dealing with constant maturity swaps (CMS).

Original language | English |
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Place of Publication | www |

Publisher | SSRN: Social Science Research Network |

Number of pages | 18 |

Publication status | Published - 16 Dec 2010 |

Series | ISEG Advance Working Paper |
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Number | No. 9 |

Volume | 2008 |

### Keywords

- Affine Term Structure
- Convexity Adjustments
- CMS
- Libor in Arrears

## Cite this

Murgoci, A., & Gaspar, R. M. (2010).

*Convexity Adjustments for ATS Models*. SSRN: Social Science Research Network. ISEG Advance Working Paper, No. No. 9, Vol.. 2008 http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1399323