Continuous-time term structure models: Forward measure approach |
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Authors: | Marek Musiela Marek Rutkowski |
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Institution: | (1) School of Mathematics, University of New South Wales, Sydney 2052, NSW, Australia (e-mail: musiela@solution.maths.unsw.edu.au) , AU;(2) Institute of Mathematics, Politechnika Warszawska, PL-00-661 Warszawa, Poland (e-mail: markrut@alpha.im.pw.edu.pl) , PL |
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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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Keywords: | : Term structure of interest rates forward measure martingale measure LIBOR rate JEL classification:E43 E44 Mathematics Subject Classification (1991): 60G44 60H30 90A09 |
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