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A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton

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  • Alan Brace
  • Marek Musiela

Abstract

Working within the Heath-Jarrow-Morton framework and using the theory of stochastic equations in infinite dimensions, a useful multifactor Gauss-Markov model for the movement of the whole of the yield curve is derived. Swaptions are priced. They are hedged by eliminating random terms between the semimartingale representations of the swaption and hedging instruments. Hedging efficiency is analyzed. the model is fitted to the swap/cap strips in Australia. Computation times on a 20-MHz laptop computer are acceptable. Copyright 1994 Blackwell Publishers.

Suggested Citation

  • Alan Brace & Marek Musiela, 1994. "A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 259-283.
  • Handle: RePEc:bla:mathfi:v:4:y:1994:i:3:p:259-283
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9965.1994.tb00095.x
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    Citations

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    Cited by:

    1. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348.
    2. Junwu Gan, 2014. "An almost Markovian LIBOR market model calibrated to caps and swaptions," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1937-1959, November.
    3. Björk, Tomas, 2000. "A Geometric View of Interest Rate Theory," SSE/EFI Working Paper Series in Economics and Finance 419, Stockholm School of Economics, revised 21 Dec 2000.
    4. Carl Chiarella & Oh-Kang Kwon, 2000. "A Class of Heath-Jarrow-Morton Term Structure Models with Stochastic Volatility," Research Paper Series 34, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Bjork, Tomas & Christensen, Bent Jesper & Gombani, Andrea, 1998. "Some system theoretic aspects of interest rate theory," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 17-23, May.
    6. Giuseppe Arbia & Michele Di Marcantonio, 2015. "Forecasting Interest Rates Using Geostatistical Techniques," Econometrics, MDPI, Open Access Journal, vol. 3(4), pages 1-28, November.
    7. Munk, Claus & Sorensen, Carsten, 2004. "Optimal consumption and investment strategies with stochastic interest rates," Journal of Banking & Finance, Elsevier, vol. 28(8), pages 1987-2013, August.
    8. Chiarella, Carl & Clewlow, Les & Musti, Silvana, 2005. "A volatility decomposition control variate technique for Monte Carlo simulations of Heath Jarrow Morton models," European Journal of Operational Research, Elsevier, vol. 161(2), pages 325-336, March.
    9. João Pedro Vidal Nunes & Pedro Miguel Silva Prazeres, 2014. "Pricing Swaptions Under Multifactor Gaussian Hjm Models," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 762-789, October.
    10. João Nunes, 2011. "American options and callable bonds under stochastic interest rates and endogenous bankruptcy," Review of Derivatives Research, Springer, vol. 14(3), pages 283-332, October.
    11. Falini, Jury, 2010. "Pricing caps with HJM models: The benefits of humped volatility," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1358-1367, December.
    12. Tappe, Stefan, 2016. "Affine realizations with affine state processes for stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2062-2091.
    13. Dai, Qiang & Singleton, Kenneth J., 2003. "Fixed-income pricing," Handbook of the Economics of Finance,in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 20, pages 1207-1246 Elsevier.
    14. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2016. "The stochastic string model as a unifying theory of the term structure of interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 217-237.
    15. Meifang Chu, 1997. "The Random Yield Curve and Interest Rate Options," Finance 9710003, EconWPA.
    16. Björk, Tomas & Gombani, Andrea, 1997. "Minimal Realizations of Forward Rates," SSE/EFI Working Paper Series in Economics and Finance 182, Stockholm School of Economics.
    17. Stefan Tappe & Stefan Weber, 2014. "Stochastic mortality models: an infinite-dimensional approach," Finance and Stochastics, Springer, vol. 18(1), pages 209-248, January.
    18. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
    19. João Pedro Vidal Nunes & Luís Alberto Ferreira De Oliveira, 2007. "Multifactor and analytical valuation of treasury bond futures with an embedded quality option," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(3), pages 275-303, March.
    20. Camilla Landén & Tomas Björk, 2002. "On the construction of finite dimensional realizations for nonlinear forward rate models," Finance and Stochastics, Springer, vol. 6(3), pages 303-331.

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