Chebyshev polynomial approximation to approximate partial differential equations
This pa per suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.
|Date of creation:||Mar 2008|
|Date of revision:|
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- 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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- Avinash Dixit, 1992. "Investment and Hysteresis," Journal of Economic Perspectives, American Economic Association, vol. 6(1), pages 107-132, Winter.
- Sullivan, Michael A, 2000. "Valuing American Put Options Using Gaussian Quadrature," Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 75-94.
- Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December.
- Manuel Moreno & Javier R. Navas, 2001.
"On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives,"
Economics Working Papers
543, Department of Economics and Business, Universitat Pompeu Fabra.
- Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
- Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-47.
- Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-20, June.
- Lars Stentoft, 2004. "Assessing the Least Squares Monte-Carlo Approach to American Option Valuation," Review of Derivatives Research, Springer, vol. 7(2), pages 129-168, 08.
- Breen, Richard, 1991. "The Accelerated Binomial Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(02), pages 153-164, June.
- Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
- Abadir, Karim M. & Rockinger, Michael, 2003. "Density Functionals, With An Option-Pricing Application," Econometric Theory, Cambridge University Press, vol. 19(05), pages 778-811, October.
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