Mathematical Finance

ON FINITE DIMENSIONAL REALIZATIONS OF TWO‐COUNTRY INTEREST RATE MODELS

Journal Article

This paper explores how consistent two‐dimensional families of forward rate curves can be constructed on an international market. Applying the approach in Björk and Christenssen (1999) and Björk and Svensson (2001), we study when a system of inherently infinite dimensional domestic and foreign forward rate processes in a two‐country economy with spot (forward) exchange rate possesses finite dimensional realizations. In the system with the forward exchange rate, the forward interest rate equations are supplemented by a third infinite dimensional stochastic differential equation representing the forward exchange rate dynamics. We construct and fit consistent families to observed Euro and USD yields as well as the forward (spot) EUR/USD exchange rate.

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