Extrapolation of Interest Rates in Semi-Annual and Monthly LMM
Document ID: 2006-21 (previously 2006/023)
Published on: 1st November 2006
Author: Colin Holmes, Martin Skrk
Within ESG 5.4.6 (and previous versions), the extrapolation of forward rates beyond the longest maturity simulated was incorrectly specified in the case of the semi-annual and monthly LMM. In our standard calibration, we provide forward rates with expiries up to 60 years. In this case, at t=0, spot rates/zc prices beyond a maturity of 60+d years rely on the extrapolation where d is the timestep corresponding to the version of the LMM used. The point on the yield curve at which the extrapolation begins decreases as the simulation progesses: for example, at t=1 year spot rates beyond 59+d years are extrapolated at t=60 years, the longest maturity ZC bond which does not rely upon the extrapolation has maturity d. Whilst we do not recommend the use of this extrapolation, this note quantifies the effect of the mis-specification.
