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Pricing Interest Rate Derivatives in a Multifactor HJM Model with Time

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We investigate the partial differential equation (PDE) for pricing interest derivatives in the multi-factor Cheyette Model, which involves time-dependent volatility functions with a special structure. The high dimensional parabolic PDE that results is solved numerically via a modified sparse grid approach, that turns out to be accurate and efficient. In addition we study the corresponding Monte Carlo simulation, which is fast since the distribution of the state variables can be calculated explicitly. The results obtained from both methodologies are compared to the known analytical solutions for bonds and caplets. When there is no analytical solution, both European and Bermudan swaptions have been evaluated using the sparse grid PDE approach that is shown to outperform the Monte Carlo simulation.

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  • Ingo Beyna & Carl Chiarella & Boda Kang, 2012. "Pricing Interest Rate Derivatives in a Multifactor HJM Model with Time," Research Paper Series 317, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:317
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    1. R. Bhar & C. Chiarella, 1997. "Transformation of Heath?Jarrow?Morton models to Markovian systems," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 1-26, March.
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    4. 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..
    5. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239, April.
    6. Marc Henrard, 2003. "Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model," Finance 0310009, University Library of Munich, Germany.
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    Cited by:

    1. Marcin Dec, 2019. "Markovian and multi-curve friendly parametrisation of a HJM model used in valuation adjustment of interest rate derivatives," Bank i Kredyt, Narodowy Bank Polski, vol. 50(2), pages 107-148.

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    Keywords

    Cheyette model; Gaussian HJM; multi-factor model; PDE valuation; sparse grid; Monte Carlo simulation;
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