Continuous-time term structure models: Forward measure approach
Marek Musiela , Marek Rutkowski
AbstractThe 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.
|Journal series||Finance and Stochastics, ISSN 0949-2984|
|Keywords in English||Key words: Term structure of interest rates, forward measure, martingale measure, LIBOR rate JEL classification:E43, E44 Mathematics Subject Classification (1991): 60G44, 60H30, 90A09|
|ASJC Classification||; ;|
|Publication indicators||: 2005 = 2.319; : 2006 = 1.267 (2) - 2007=1.442 (5)|
|Citation count*||191 (2015-05-30)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.