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A multicurrency extension of the lognormal interest rate Market Models

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  • Erik Schlögl

    (School of Finance and Economics, University of Technology, Sydney, NSW 2007 Australia Manuscript)

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 no-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.

Suggested Citation

  • Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
    • Handle: RePEc:spr:finsto:v:6:y:2002:i:2:p:173-196
    Note: received: July 1999; final version received: May 2001
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    References listed on IDEAS

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    More about this item

    Keywords

    Lognormal LIBOR models; term structure of interest rates; currency options; interest rate options; change of measure;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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