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A Multicurrency Extension of the Lognormal Interest Rate Market Models

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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 swap rates in two currencies, for one maturity, with the dynamics for all other maturities given by no-arbitage 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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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 20.

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Date of creation: 01 Aug 1999
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Handle: RePEc:uts:rpaper:20

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  1. 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.
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  5. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
  6. Rudiger Frey & Daniel Sommer, 1996. "A systematic approach to pricing and hedging international derivatives with interest rate risk: analysis of international derivatives under stochastic interest rates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(4), pages 295-317.
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  9. Sandmann,Klaus & Sondermann,Dieter, . "A term structure model and the pricing of interest rate options," Discussion Paper Serie B 129, University of Bonn, Germany.
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Cited by:
  1. Ernst Eberlein & Wolfgang Kluge & Antonis Papapantoleon, 2006. "Symmetries In Lévy Term Structure Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(06), pages 967-986.
  2. Maria Siopacha & Josef Teichmann, 2010. "Weak and strong Taylor methods for numerical solutions of stochastic differential equations," Quantitative Finance, Taylor & Francis Journals, vol. 11(4), pages 517-528.
  3. Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2011. "Efficient and accurate log-L\'evy approximations to L\'evy driven LIBOR models," Papers 1106.0866, arXiv.org, revised Jan 2012.
  4. Philipp J. Schönbucher, 2000. "A Libor Market Model with Default Risk," Bonn Econ Discussion Papers bgse15_2001, University of Bonn, Germany.
  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.
  6. Maria Siopacha & Josef Teichmann, 2007. "Weak and Strong Taylor methods for numerical solutions of stochastic differential equations," Papers 0704.0745, arXiv.org.
  7. Antonis Papapantoleon, 2009. "Old and new approaches to LIBOR modeling," Papers 0910.4941, arXiv.org, revised Apr 2010.
  8. 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.
  9. Raoul Pietersz & Marcel van Regenmortel, 2005. "Generic Market Models," Finance 0502009, EconWPA.
    • Pietersz, R. & van Regenmortel, M., 2005. "Generic Market Models," ERIM Report Series Research in Management ERS-2005-010-F&A, 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.
  10. Lech A. Grzelak & Cornelis W. Oosterlee, 2012. "On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(1), pages 1-35, February.
  11. Kay Pilz & Erik Schlogl, 2009. "A Hybrid Commodity and Interest Rate," Research Paper Series 261, Quantitative Finance Research Centre, University of Technology, Sydney.
  12. Vincenzo Costa, 2004. "Risk neutral valuation and uncovered interest rate parity in a stochastic two-country-economy with two goods," Economics Bulletin, AccessEcon, vol. 3(43), pages 1-10.
  13. 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.
  14. Antonis Papapantoleon & Maria Siopacha, 2009. "Strong Taylor approximation of stochastic differential equations and application to the L\'evy LIBOR model," Papers 0906.5581, arXiv.org, revised Oct 2010.
  15. Fabio Mercurio, 2005. "Pricing inflation-indexed derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 289-302.
  16. Akihiko Takahashi & Kohta Takehara, 2007. "An Asymptotic Expansion Approach to Currency Options with a Market Model of Interest Rates under Stochastic Volatility Processes of Spot Exchange Rates," Asia-Pacific Financial Markets, Springer, vol. 14(1), pages 69-121, March.
  17. A. Pelsser, 2003. "Mathematical foundation of convexity correction," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 59-65.
  18. Antonis Papapantoleon & David Skovmand, 2010. "Picard approximation of stochastic differential equations and application to LIBOR models," Papers 1007.3362, arXiv.org, revised Jul 2011.
  19. A. Antonov & T. Misirpashaev, 2009. "Markovian Projection Onto A Displaced Diffusion: Generic Formulas With Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 507-522.
  20. Mikkelsen, Peter, 2001. "Cross-Currency LIBOR Market Models," Finance Working Papers 01-6, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  21. Ernst Eberlein & Fehmi Özkan, 2005. "The Lévy LIBOR model," Finance and Stochastics, Springer, vol. 9(3), pages 327-348, 07.
  22. Ernst Eberlein & Nataliya Koval, 2006. "A cross-currency Levy market model," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 465-480.

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