A multicurrency extension of the lognormal interest rate market models (Q1849789)

The author considers the market models of the term structure of interest rates in the multicurrency case. The forward LIBOR or forward swap rates are assumed to be lognormal under the forward probability measure of the corresponding maturity. If the forward LIBOR or the forward swap rates in the two currencies cases are lognormal, then the forward exchange rate linking the two currencies can only be chosen to be lognormal for one maturity and for all other maturities the dynamics are given by no-arbitrage relationships. If forward interest rates of domestic currency and all forward exchange rates are given by lognormal dynamic, then dynamics of the foreign interest rates is determined by no-arbitrage relationships.