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

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Author Info
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)
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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Publisher Info
Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 1 (1997)
Issue (Month): 4 ()
Pages: 261-291
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Handle: RePEc:spr:finsto:v:1:y:1997:i:4:p:261-291

Note: received: July 1996; final version received: October 1996
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Related research
Keywords: Term structure of interest rates; forward measure; martingale measure; LIBOR rate;

Find related papers by JEL classification:
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates
E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Jesús P. Colino & Winfried Stute, 2008. "Credit risk with semimartingales and risk-neutrality," Statistics and Econometrics Working Papers ws085417, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
  2. Erik Schlögl, 2001. "Arbitrage-Free Interpolation in Models of Market Observable Interest Rates," Research Paper Series 71, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  3. Grace Kuan, 2000. "Recovering Local Volatility Functions Of Forward Libor Rates," Computing in Economics and Finance 2000 255, Society for Computational Economics. [Downloadable!]
  4. Klaas Schulze, 2008. "Asymptotic Maturity Behavior of the Term Structure," Bonn Econ Discussion Papers bgse11_2008, University of Bonn, Germany. [Downloadable!]
  5. Dudenhausen, Antje & Erik Schloegl & Lutz Schloegl, 1999. "Robustness of Gaussian Hedges and the Hedging of Fixed Income Derivatives," Discussion Paper Serie B 422, University of Bonn, Germany, revised Apr 1999. [Downloadable!]
    Other versions:
  6. Erik Schlögl, 1999. "A Multicurrency Extension of the Lognormal Interest Rate Market Models," Research Paper Series 20, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
    Other versions:
  7. Christian Zühlsdorff, 2002. "Extended Libor Market Models with Affine and Quadratic Volatility," Bonn Econ Discussion Papers bgse6_2002, University of Bonn, Germany. [Downloadable!]
  8. Raoul Pietersz & Marcel van Regenmortel, 2005. "Generic Market Models," Finance 0502009, EconWPA. [Downloadable!]
    Other versions:
    • Pietersz, R. & Regenmortel, M. van, 2005. "Generic Market Models," Research Paper ERS-2005-010-F&A Revision, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus Uni. [Downloadable!]
  9. Erik Schlögl, 2002. "Extracting the Joint Volatility Structure of Foreign Exchange and Interest Rates from Option Prices," Research Paper Series 79, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  10. Raoul Pietersz & Antoon Pelsser & Marcel van Regenmortel, 2005. "Fast drift approximated pricing in the BGM model," Finance 0502005, EconWPA. [Downloadable!]
  11. Marek Rutkowski, 1999. "Models of forward Libor and swap rates," Applied Mathematical Finance, Taylor and Francis Journals, vol. 6(1), pages 29-60, March. [Downloadable!] (restricted)
  12. Massoud Heidari & Liuren Wu, 2002. "Term Structure of Interest Rates, Yield Curve Residuals, and the Consistent Pricing of Interest Rates and Interest Rate Derivatives," Finance 0207010, EconWPA, revised 05 Sep 2002. [Downloadable!]
  13. Tim Dunn & Erik Schlögl & Geoff Barton, 2000. "Simulated Swaption Delta-Hedging in the Lognormal Forward Libor Model," Research Paper Series 40, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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