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Multiple curve Lévy forward price model allowing for negative interest rates
Author(s) -
Eberlein Ernst,
Gerhart Christoph,
Grbac Zorana
Publication year - 2020
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12210
Subject(s) - libor market model , valuation (finance) , interest rate , multiplicative function , forward rate , econometrics , lévy process , libor , measure (data warehouse) , interest rate derivative , fourier transform , yield curve , calibration , computer science , economics , mathematics , statistics , finance , mathematical analysis , database
Abstract In this paper, we develop a framework for discretely compounding interest rates that is based on the forward price process approach. This approach has a number of advantages, in particular in the current market environment. Compared to the classical as well as the Lévy Libor market model, it allows in a natural way for negative interest rates and has superb calibration properties even in the presence of extremely low rates. Moreover, the measure changes along the tenor structure are significantly simplified. These properties make it an excellent base for a postcrisis multiple curve setup. Two variants for multiple curve constructions based on the multiplicative spreads are discussed. Time‐inhomogeneous Lévy processes are used as driving processes. An explicit formula for the valuation of caps is derived using Fourier transform techniques. Relying on the valuation formula, we calibrate the two model variants to market data.