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Multiple curve Lévy forward price model allowing for negative interest rates

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  • Ernst Eberlein
  • Christoph Gerhart
  • Zorana Grbac

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.

Suggested Citation

  • Ernst Eberlein & Christoph Gerhart & Zorana Grbac, 2020. "Multiple curve Lévy forward price model allowing for negative interest rates," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 167-195, January.
    • Handle: RePEc:bla:mathfi:v:30:y:2020:i:1:p:167-195
    DOI: 10.1111/mafi.12210
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    Cited by:

    1. Basse, Tobias & Wegener, Christoph, 2022. "Inflation expectations: Australian consumer survey data versus the bond market," Journal of Economic Behavior & Organization, Elsevier, vol. 203(C), pages 416-430.
    2. Alessandro Gnoatto & Silvia Lavagnini, 2023. "Cross-Currency Heath-Jarrow-Morton Framework in the Multiple-Curve Setting," Papers 2312.13057, arXiv.org.
    3. Gerhart, Christoph & Lütkebohmert, Eva, 2020. "Empirical analysis and forecasting of multiple yield curves," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 59-78.

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