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On the valuation of compositions in Lévy term structure models. (English) Zbl 1182.91184

Summary: 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.

MSC:

91G30 Interest rates, asset pricing, etc. (stochastic models)
91G20 Derivative securities (option pricing, hedging, etc.)
60G51 Processes with independent increments; Lévy processes
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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