The Libor Market Model: from theory to calibration

Riga, Candia (2011) The Libor Market Model: from theory to calibration. [Laurea magistrale], Università di Bologna, Corso di Studio in Matematica [LM-DM270]
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This thesis is focused on the financial model for interest rates called the LIBOR Market Model. In the appendixes, we provide the necessary mathematical theory. In the inner chapters, firstly, we define the main interest rates and financial instruments concerning with the interest rate models, then, we set the LIBOR market model, demonstrate its existence, derive the dynamics of forward LIBOR rates and justify the pricing of caps according to the Black’s formula. Then, we also present the Swap Market Model, which models the forward swap rates instead of the LIBOR ones. Even this model is justified by a theoretical demonstration and the resulting formula to price the swaptions coincides with the Black’s one. However, the two models are not compatible from a theoretical point. Therefore, we derive various analytical approximating formulae to price the swaptions in the LIBOR market model and we explain how to perform a Monte Carlo simulation. Finally, we present the calibration of the LIBOR market model to the markets of both caps and swaptions, together with various examples of application to the historical correlation matrix and the cascade calibration of the forward volatilities to the matrix of implied swaption volatilities provided by the market.

Tipologia del documento
Tesi di laurea (Laurea magistrale)
Autore della tesi
Riga, Candia
Relatore della tesi
Corso di studio
Curriculum B: Applicativo
Ordinamento Cds
Parole chiave
Libor market model, interest rate derivatives, forward libor rates, calibration of libor market model
Data di discussione della Tesi
24 Giugno 2011

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