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Fast delta computations in the swap-rate market model

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  • Joshi, Mark
  • Yang, Chao

Abstract

We develop an efficient algorithm to implement the adjoint method that computes sensitivities of an interest rate derivative to different underlying rates in the co-terminal swap-rate market model. The order of computation per step of the new method is shown to be proportional to the number of rates times the number of factors, which is the same as the order in the LIBOR market model.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 35 (2011)
Issue (Month): 5 (May)
Pages: 764-775

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Handle: RePEc:eee:dyncon:v:35:y:2011:i:5:p:764-775

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Web page: http://www.elsevier.com/locate/jedc

Related research

Keywords: Adjoint method Delta Computational order Market model Monte Carlo simulation;

References

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  1. 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.
  2. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
  3. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
  4. Okten, Giray & Eastman, Warren, 2004. "Randomized quasi-Monte Carlo methods in pricing securities," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2399-2426, December.
  5. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
  6. S.Galluccio & Z. Huang & J.-M. Ly & O. Scaillet, 2005. "Theory and Calibration of Swap Market Models," FAME Research Paper Series rp107, International Center for Financial Asset Management and Engineering.
  7. Mark Joshi & Chao Yang, 2010. "Fast And Accurate Pricing And Hedging Of Long-Dated Cms Spread Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 839-865.
  8. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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Citations

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Cited by:
  1. Jos\'e Da Fonseca & Alessandro Gnoatto & Martino Grasselli, 2012. "A flexible matrix Libor model with smiles," Papers 1203.4786, arXiv.org.
  2. Joshi, Mark & Tang, Robert, 2014. "Effective sub-simulation-free upper bounds for the Monte Carlo pricing of callable derivatives and various improvements to existing methodologies," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 25-45.
  3. Jiun Hong Chan and Mark Joshi, 2012. "Optimal Limit Methods for Computing Sensitivities of," Department of Economics - Working Papers Series 1142, The University of Melbourne.
  4. Cristian Homescu, 2011. "Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance," Papers 1107.1831, arXiv.org.

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