On the valuation of compositions in L\'evy term structure models

TL;DR

This paper develops explicit valuation formulas for a complex interest rate derivative based on LIBOR compositions, using Fourier transform methods within Le9vy-driven interest rate models.

Contribution

It introduces novel explicit pricing formulas for path-dependent derivatives in Le9vy interest rate models, applicable to both HJM and LIBOR-type frameworks.

Findings

Derived Fourier-based valuation formulas for LIBOR composition options.

Applied models driven by time-inhomogeneous Le9vy processes.

Provided explicit solutions for complex interest rate derivatives.

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 L\'evy process.