Continuous-time term structure models: Forward measure approach

Marek Musiela , Marek Rutkowski

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.
Author Marek Musiela
Marek Musiela,,
-
, Marek Rutkowski (FMIS / DSPFM)
Marek Rutkowski,,
- Department of Stochastic Processes and Financial Mathematics
Journal seriesFinance and Stochastics, ISSN 0949-2984
Issue year1997
Vol1
No4
Pages261-291
Keywords in EnglishKey words: Term structure of interest rates, forward measure, martingale measure, LIBOR rate JEL classification:E43, E44 Mathematics Subject Classification (1991): 60G44, 60H30, 90A09
ASJC Classification1804 Statistics, Probability and Uncertainty; 2003 Finance; 2613 Statistics and Probability
DOIDOI:10.1007/s007800050025
URL http://link.springer.com/article/10.1007/s007800050025
Score (nominal)35
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2005 = 2.319; WoS Impact Factor: 2006 = 1.267 (2) - 2007=1.442 (5)
Citation count*191 (2015-05-30)
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