Divergence of the Cash Account within a Lognormal Interest Rate Model
Document ID: 2007-11 (previously 2007/007)
Published on: 1st September 2007
Author: Colin Holmes, David Roseburgh
Models of interest rates commonly make the assumption that some interest rate (e.g. forward rates in a Libor Market Model or the short rate in a 2-factor Black-Karasinski model) is lognormally distributed. This ensure rates remain positive but the nature of the distribution means there is a finite probability of observing extremely large rates. This can result in a so called "exploding" cash account. Here we look at the theoretical and technical issues surrounding this phenomenon, and discuss one potential workaround capping the modelled rate at an appropriate level.
