On the valuation of compositions in Lévy term structure models

Abstract

We derive explicit valuation formulae for an exotic path-dependent interest rate derivative, namely an option on the composition of LIBOR rates. The formulae are based on Fourier transform methods for option pricing. We consider two models for the evolution of interest rates: an HJM-type forward rate model and a LIBOR-type forward price model. Both models are driven by a time-inhomogeneous Lévy process.

Keywords:

• Affine term structure models
• Applied mathematical finance
• Interest rate modelling
• Lévy process

Acknowledgements

We thank Ernst Eberlein for motivating discussions and helpful comments. Both authors gratefully acknowledge the financial support from the Deutsche Forschungsgemeinschaft (DFG, EB 66/9-2). A.P. gratefully acknowledges the financial support from the Austrian Science Fund (FWF grant Y328, START Prize).