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Title: Calibration to swaptions in the libor market model
Keywords: Interest Rates Derivatives, Libor Market Model, Calibration, Rank Reduction Methods, Swaption Approximations
Issue Date: 13-Mar-2007
Citation: PIERRE BERET (2007-03-13). Calibration to swaptions in the libor market model. ScholarBank@NUS Repository.
Abstract: In this dissertation, the Libor Market Model is presented and its calibration process is derived. We assume the Forward Libor Rates follow log-normal stochastic processes with a d-dimensional Brownian motion and build an interest rates model able to price interest rate derivatives. We emphasize how different it is from the usual short-term interest rates models (Hull-White). Nevertheless, this pricing model only makes sense if vanilla products, namely caps and European swaptions, can be well priced with respect to their market value. To check this, we propose different parametric forms of instantaneous volatilities and correlations to obtain the best results. Then, we show a method to reduce the dimensionality of the Libor Market model compared to the number of Forward rates involved by using Rebonato Angles and Frobenius norm. Finally, we derive approximations formula for European swaptions and show we can avoid Monte-Carlo simulations for the calculations of the swaptions during the calibration. Some numerical results are given on a 3 factors model. We discuss then different issues raised and current developments, more specifically the SABR skew form and cross-asset products.
Appears in Collections:Master's Theses (Open)

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