Abstract
We derive the parabolic PDE implied by the model dynamics and, in combination with terminal conditions, we can price interest rate derivatives. The initial value problem is solved numerically by the sparse grid technique based on a standard Crank Nicolson Finite Difference method with projected successive over-relaxation (PSOR). Implementing a modified sparse grid technique, we can increase the accuracy of the valuation.
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Notes
- 1.
A thorough error analysis of the multi-linear interpolation operator can be found in Reisinger (2008) who gives a generic derivation for linear difference schemes through an error correction technique employing semi-discretisations and obtains error formulae as well.
- 2.
Dr. Boda Kang; boda.kang@uts.edu.au; Finance Discipline Group, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia
- 3.
We used a Windows based PC with Intel Core TM 2 Quad CPU @ 2.66 GHz and 3.49 GB RAM.
- 4.
We used a Linux based PC with CPU Xeon X5680 @ 3.33 GHz and 24 GB RAM.
- 5.
We used the FEIT and Business F & E High Performance Computing Linux Cluster of the University of Technology Syndney.
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Beyna, I. (2013). PDE Valuation. In: Interest Rate Derivatives. Lecture Notes in Economics and Mathematical Systems, vol 666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34925-6_7
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DOI: https://doi.org/10.1007/978-3-642-34925-6_7
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