Abstract:
The Market Models of the term structure of interest rates, in which
forward LIBOR or forward swap rates are modelled to be lognormal under the
forward probability measure of the corresponding maturity, are extended to a
multicurrency setting. If lognormal dynamics are assumed for forward LIBOR or
forward swap rates in two currencies, the forward exchange rate linking the two
currencies can only be chosen to be lognormal for one maturity, with the dynamics
for all other maturities given by ncr-arbitrage relationships. Alternatively, one
could choose forward interest rates in only one currency, say the domestic, to be
lognormal and postulate lognormal dynamics for all forward exchange rates, with
the dynamics of foreign interest rates determined by no-arbitrage relationships.
