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Pricing Interest Rate Derivatives in a Multifactor HJM Model with Time

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Abstract

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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File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp317.pdf
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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 317.

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Length: 65
Date of creation: 01 Oct 2012
Date of revision:
Handle: RePEc:uts:rpaper:317

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

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  1. Marc Henrard, 2003. "Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model," Finance 0310009, EconWPA.
  2. 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.
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