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LIBOR Market Model: Implementation and Calibration
Alex Ferris
ESE 499 Senior Design Project

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Abstract

In this paper I implement and calibrate the Lognormal Forward-LIBOR Model (LFM) for the term structure of interest-rates. This model is a subset of the LIBOR Market Model class of stochastic interest-rate models and is characterized by the lognormal distribution of forward LIBOR rates under appropriate numeraires. Specifically, I implemented the LFM under two different instantaneous volatility formulations, Rebonato’s 6.21a (2002) and Brigo and Mercurio’s Formulation 7 (2006). The implementations are then calibrated to market data for Caps and Swaptions. Finally, the results are analyzed for their accuracy and their correspondence to financial theory and intuition. All implementation and calibration is done in MATLAB.

Acknowledgements

I would first like to thank Anatoliy Belaygorod for his help formulating and executing this project. His knowledge, both theoretical and practical, was extremely helpful and he was able to point me to many of the resources that I found to be invaluable. Additionally, I want to thank his Teaching Assistants for FIN 551, Linda (Meng) Xu and Alan Yang, for their assistance. They were a sounding board for my ideas and also showed me some great sources.

For this project, I was supervised by Anatoliy Belaygorod, Adjuct Professor of Finance at the Olin Business School.