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A multicurrency extension of the lognormal interest rate Market Models

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Author Info
Erik Schlögl () (School of Finance and Economics, University of Technology, Sydney, NSW 2007 Australia Manuscript)

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Abstract

The Market Models of the term structure of interest rates, in which forward LIBOR or forward swap rates are modelled to be lognormal under the forward probability measure of the corresponding maturity, are extended to a multicurrency setting. If lognormal dynamics are assumed for forward LIBOR or forward swap rates in two currencies, the forward exchange rate linking the two currencies can only be chosen to be lognormal for one maturity, with the dynamics for all other maturities given by no-arbitrage relationships. Alternatively, one could choose forward interest rates in only one currency, say the domestic, to be lognormal and postulate lognormal dynamics for all forward exchange rates, with the dynamics of foreign interest rates determined by no-arbitrage relationships.

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

Volume (Year): 6 (2002)
Issue (Month): 2 ()
Pages: 173-196
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Handle: RePEc:spr:finsto:v:6:y:2002:i:2:p:173-196

Note: received: July 1999; final version received: May 2001
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Related research
Keywords: Lognormal LIBOR models; term structure of interest rates; currency options; interest rate options; change of measure;

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Find related papers by JEL classification:
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
F31 - International Economics - - International Finance - - - Foreign Exchange
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates

References listed on IDEAS
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. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January. [Downloadable!] (restricted)
  2. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330. [Downloadable!] (restricted)
  3. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-30, March. [Downloadable!] (restricted)
    Other versions:
  4. Sandmann,Klaus & Sondermann,Dieter, . "A term structure model and the pricing of interest rate options," Discussion Paper Serie B 129, University of Bonn, Germany.
  5. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June. [Downloadable!] (restricted)
  6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  7. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291. [Downloadable!] (restricted)
Full references

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. Antonis Papapantoleon, 2009. "Old and new approaches to LIBOR modeling," Quantitative Finance Papers 0910.4941, arXiv.org. [Downloadable!]
  2. Samson Assefa, 2007. "Calibration and Pricing in a Multi-Factor Quadratic Gaussian Model," Research Paper Series 197, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  3. Maria Siopacha & Josef Teichmann, 2007. "Weak and Strong Taylor methods for numerical solutions of stochastic differential equations," Quantitative Finance Papers 0704.0745, arXiv.org. [Downloadable!]
  4. 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!]
  5. 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!]
  6. Antonis Papapantoleon & Maria Siopacha, 2009. "Strong Taylor approximation of Stochastic Differential Equations and application to the L\'evy LIBOR model," Quantitative Finance Papers 0906.5581, arXiv.org. [Downloadable!]
  7. 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!]
  8. Ernst Eberlein & Nataliya Koval, 2006. "A cross-currency Lévy market model," Quantitative Finance, Taylor and Francis Journals, vol. 6(6), pages 465-480, December. [Downloadable!] (restricted)
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