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Analysing Quantiles in Models of Forward Term Rates

Author

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  • Thomas A. McWalter

    (The African Institute of Financial Markets and Risk Management (AIFMRM), University of Cape Town, Cape Town 7701, South Africa
    Faculty of Science, Department of Statistics, University of Johannesburg, Johannesburg 2006, South Africa)

  • Erik Schlögl

    (The African Institute of Financial Markets and Risk Management (AIFMRM), University of Cape Town, Cape Town 7701, South Africa
    Faculty of Science, Department of Statistics, University of Johannesburg, Johannesburg 2006, South Africa
    School of Mathematical and Physical Sciences, University of Technology Sydney, Ultimo, NSW 2007, Australia)

  • Jacques van Appel

    (Faculty of Science, Department of Statistics, University of Johannesburg, Johannesburg 2006, South Africa)

Abstract

The class of forward-LIBOR market models can, under certain volatility structures, produce unrealistically high long-dated forward rates, particularly for maturities and tenors beyond the liquid market calibration instruments. This paper presents a diagnostic tool for analysing the quantiles of distributions for forward term rates in a displaced lognormal forward-LIBOR model (DLFM). In particular, we provide a quantile approximation that can be used to assess whether the modelled term rates remain within realistic bounds with a high probability. Applying this diagnostic tool (verified using Quasi-Monte Carlo (QMC) simulations), we show that realised forward term rates for long time horizons may be kept within realistic limits by appropriately damping the tail of the DLFM volatility function.

Suggested Citation

  • Thomas A. McWalter & Erik Schlögl & Jacques van Appel, 2023. "Analysing Quantiles in Models of Forward Term Rates," Risks, MDPI, vol. 11(2), pages 1-18, January.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:2:p:29-:d:1049181
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    References listed on IDEAS

    as
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