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Arbitrage-Free Interpolation in Models of Market Observable Interest Rates

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Abstract

Models which postulate lognormal dynamics for interest rates which are compounded according to market conventions, such as forward LIBOR or forward swap rates, can be constructed initially in a discrete tenor framework. Interpolating interest interest rates between maturities in the discrete tenor structure is equivalent to extending the model to continuous tenor. The present paper sets forth an alternative way of performing this extension; one which preserves the Markovian properties of the discrete tenor models and guarantees the positivity of all interpolated rates.

Suggested Citation

  • 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.
  • Handle: RePEc:uts:rpaper:71
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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp71.pdf
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    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    4. 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 409-430, March.
    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. Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    7. repec:wsi:ijtafx:v:04:y:2001:i:04:n:s0219024901001127 is not listed on IDEAS
    8. 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 637-654, May-June.
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    11. Tim Dun & Geoff Barton & Erik Schlögl, 2001. "Simulated Swaption Delta–Hedging In The Lognormal Forward Libor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(04), pages 677-709.
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    Cited by:

    1. Yang Chang, 2014. "A Consistent Approach to Modelling the Interest Rate Market Anomalies Post the Global Financial Crisis," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 18, january-d.
    2. Yang Chang & Erik Schlogl, 2014. "A Consistent Framework for Modelling Basis Spreads in Tenor Swaps," Research Paper Series 348, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. 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.
    4. 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.
    5. Kay Pilz & Erik Schlogl, 2010. "Calibration of Multicurrency LIBOR Market Models," Research Paper Series 286, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Grzelak, Lech & Oosterlee, Kees, 2010. "An Equity-Interest Rate Hybrid Model With Stochastic Volatility and the Interest Rate Smile," MPRA Paper 20574, University Library of Munich, Germany.
    7. Raoul Pietersz & Marcel Regenmortel, 2006. "Generic market models," Finance and Stochastics, Springer, vol. 10(4), pages 507-528, December.
      • Raoul Pietersz & Marcel van Regenmortel, 2005. "Generic Market Models," Finance 0502009, University Library of Munich, Germany.
      • 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 University Rotterdam.
    8. repec:wsi:ijtafx:v:17:y:2014:i:01:n:s0219024914500010 is not listed on IDEAS
    9. K. F. Pilz & E. Schlögl, 2013. "A hybrid commodity and interest rate market model," Quantitative Finance, Taylor & Francis Journals, vol. 13(4), pages 543-560, March.

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