Dissertation: Extended Libor Market Models

Extended Libor Market Models

Derivatives Pricing, Implementation, and Calibration

Finanzmanagement, volume 7

Hamburg , 118 pages

ISBN 978-3-8300-0710-4 (print)

about this book

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During the last 20 years the use of financial derivatives as well as quantitative research has grown steadily. For the modelization of interest rate risk, the focus of academic research has shifted to the Libor market model. It is also used by practitioners in financial institutions around the globe. It ows its popularity to a remarkable property: it offers a well-founded derivation of the Black formula in the theory of financial economics. The Black formula is the market standard to price the most important interest rate option, the cap.

Across strikes and maturities, observed interest rate option prices deviate from the values predicted by the lognormal Libor market model. In this book, the author presents extensions of the model which are better suited to capture these deviations. These extended models offer closed form pricing formulae for caps and swaptions, and fit observed market prices better as well.

The lognormal stochastic model for an asset uses a linear function for the volatility. The first part of this thesis extends this setup to general quadratic functions. It is still possible to find closed form pricing formulae for options, so there is no need to use numerical or Monte-Carlo methods.

The second part applies these results to the Libor market model. Next to new cap pricing formulae, it is shown that the extended model allows for an approximative swaption pricing formula whose properties are carefully studied. A swaption is an option on a swap rate, a derivative as important as caps in the market. Finally, different specifications are calibrated to data from the German market.

Ihr Werk im Verlag Dr. Kovač

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