A Multicurrency Extension of the Lognormal Interest Rate Market Models

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 swap rates in two currencies, for one maturity, with the dynamics for all other maturities given by no-arbitage 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.