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

Marek Rutkowski () and Marek Musiela ()
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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

Finance and Stochastics, 1997, vol. 1, issue 4, 261-291

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.

Keywords: Term structure of interest rates; forward measure; martingale measure; LIBOR rate (search for similar items in EconPapers)
JEL-codes: E43 E44 (search for similar items in EconPapers)
Date: 1997-09-30
Note: received: July 1996; final version received: October 1996
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