ISSN:
1432-1122
Keywords:
Key words: Term structure of interest rates, forward measure, martingale measure, LIBOR rate JEL classification:E43, E44 Mathematics Subject Classification (1991): 60G44, 60H30, 90A09
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Economics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s007800050025
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