Using Chebyshev polynomials to approximate partial differential equations

Computational Economics

Volumn 35, Issue 3, 2010, Pages 235-244

  Caporale, Guglielmo Maria ^a   Cerrato, Mario ^b  

^a BRUNEL UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

Chebyshev nodes; Chebyshev polynomial approximation; European options

Indexed keywords

EID: 83555179950     PISSN: 09277099     EISSN: 15729974     Source Type: Journal    
DOI: 10.1007/s10614-009-9172-8     Document Type: Article

References (13)

1. Abadir, K., & Rockinger, M. (2003). Density functionals, with an option-pricing application. Econometric Theory, 19, 778-811.
2. Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. The Journal of Political Economy, 81, 637-654. doi:10.1086/260062.
3. Chang, C., Chung, C. S., & Stapleton, R. C. (2002). Richardson extrapolation techniques for the pricing of American-style options. Department of Finance, The Management School, National Central University, Taiwan, Working Paper No. 3.
4. Dangl, T., & Wirl, F. (2004). Investment under uncertainty: Calculating the value function when the Bellman equation cannot be solved analytically. Journal of Economic Dynamics & Control, 28(7), 1437-1460. doi:10.1016/S0165-1889(03)00110-6.
5. Dixit, A. (1992). Investment and hysteresis. The Journal of Economic Perspectives, 6, 107-132.
6. Dixit, A., & Pindyck, S. (1994). Investment under uncertainty. Princeton: Princeton University Press.
7. Judd, K. (1998). Numerical methods in economics. Amherst: Massachusetts Institute of Technology Press.
8. Longstaff, F. A., & Schwartz, E. S. (2001). Valuing American options by simulation: A simple least-squares approach. Review of Financial Studies, 14(1), 113-147. doi:10.1093/rfs/14.1.113.
9. Miranda, M., & Fackler, P. (2002). Applied computational economics and finance. Cambridge: MIT Press.
10. Pindyck, R. S. (1991) Irreversibility and the explanation of the investment behaviour. In D. Lund & B. Oksendal (Eds.), Stochastic models and option values. Amsterdam, North Holland.
11. Rivlin, T. J. (1990). Chebyshev polynomials: From approximation theory to algebra and number theory (2nd ed.). New York: John Wiley and Sons.
12. Tzavalis, E., & Wang, S. (2003). Pricing American options under stochastic volatility: A new method using Chebyshev polinomials to approximate the early exercise boundary. Working Paper No. 488, Queen Mary, University of London, Department of Economics.
13. Werther, T. (1993). Generalized Vandermode determinants over the Chebyshev basis. International Computer Science Institute, 1947, Center Street, Berkeley, California.