Analysing Quantiles in Models of Forward Term Rates

Thomas A. McWalter, Erik Schlogl and Jacques van Appel ()
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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
Jacques van Appel: Faculty of Science, Department of Statistics, University of Johannesburg, Johannesburg 2006, South Africa

Risks, 2023, vol. 11, issue 2, 1-18

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.

Keywords: interest rate modelling; forward term rates; LIBOR market model; model calibration (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:11:y:2023:i:2:p:29-:d:1049181

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