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A Fourier interpolation method for numerical solution of FBSDEs: Global convergence, stability, and higher order discretizations

Listed author(s):
  • Polynice Oyono Ngou
  • Cody Hyndman
Registered author(s):

    The implementation of the convolution method for the numerical solution of backward stochastic differential equations (BSDEs) introduced in [19] uses a uniform space grid. Locally, this approach produces a truncation error, a space discretization error, and an additional extrapolation error. Even if the extrapolation error is convergent in time, the resulting absolute error may be high at the boundaries of the uniform space grid. In order to solve this problem, we propose a tree-like grid for the space discretization which suppresses the extrapolation error leading to a globally convergent numerical solution for the (F)BSDE. On this alternative grid the conditional expectations involved in the BSDE time discretization are computed using Fourier analysis and the fast Fourier transform (FFT) algorithm as in the initial implementation. The method is then extended to higher-order time discretizations of FBSDEs. Numerical results demonstrating convergence are also presented.

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    File URL: http://arxiv.org/pdf/1410.8595
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    Paper provided by arXiv.org in its series Papers with number 1410.8595.

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    Date of creation: Oct 2014
    Date of revision: Jun 2016
    Handle: RePEc:arx:papers:1410.8595
    Contact details of provider: Web page: http://arxiv.org/

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    4. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    5. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    6. Bender, Christian & Denk, Robert, 2007. "A forward scheme for backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1793-1812, December.
    7. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    8. Vlad Bally & Gilles Pag├Ęs & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 119-168.
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