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

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  • Alan Brace
  • Marek Musiela
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    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.

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 4 (1994)
    Issue (Month): 3 ()
    Pages: 259-283

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    Handle: RePEc:bla:mathfi:v:4:y:1994:i:3:p:259-283

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    Cited by:
    1. Björk, Tomas & Gombani, Andrea, 1997. "Minimal Realizations of Forward Rates," Working Paper Series in Economics and Finance 182, Stockholm School of Economics.
    2. 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.
    3. Stefan Tappe & Stefan Weber, 2014. "Stochastic mortality models: an infinite-dimensional approach," Finance and Stochastics, Springer, vol. 18(1), pages 209-248, January.
    4. Björk, Tomas, 2000. "A Geometric View of Interest Rate Theory," Working Paper Series in Economics and Finance 419, Stockholm School of Economics, revised 21 Dec 2000.
    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. 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.
    7. Meifang Chu, 1997. "The Random Yield Curve and Interest Rate Options," Finance 9710003, EconWPA.
    8. Sørensen, Carsten & Munk, Claus, 2001. "Optimal Consumption and Investment Strategies with Stochastic Interest Rates ," Working Papers 2000-9, Copenhagen Business School, Department of Finance.
    9. 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.
    10. 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.
    11. Björk, Tomas & Christensen, Bent Jesper, 1997. "Interest Rate Dynamics and Consistent Forward Rate Curves," Working Paper Series in Economics and Finance 209, Stockholm School of Economics.

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