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Continuous-time term structure models: Forward measure approach (*)

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  • Marek Rutkowski

    ()
    (Institute of Mathematics, Politechnika Warszawska, PL-00-661 Warszawa, Poland)

  • Marek Musiela

    ()
    (School of Mathematics, University of New South Wales, Sydney 2052, NSW, Australia)

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    Abstract

    The problem of term structure of interest rates modelling is considered in a continuous-time framework. The emphasis is on the bond prices, forward bond prices and so-called LIBOR rates, rather than on the instantaneous continuously compounded rates as in most traditional models. Forward and spot probability measures are introduced in this general set-up. Two conditions of no-arbitrage between bonds and cash are examined. A process of savings account implied by an arbitrage-free family of bond prices is identified by means of a multiplicative decomposition of semimartingales. The uniqueness of an implied savings account is established under fairly general conditions. The notion of a family of forward processes is introduced, and the existence of an associated arbitrage-free family of bond prices is examined. A straightforward construction of a lognormal model of forward LIBOR rates, based on the backward induction, is presented.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 1 (1997)
    Issue (Month): 4 ()
    Pages: 261-291

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    Handle: RePEc:spr:finsto:v:1:y:1997:i:4:p:261-291

    Note: received: July 1996; final version received: October 1996
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    Related research

    Keywords: Term structure of interest rates; forward measure; martingale measure; LIBOR rate;

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