Convergence of numerical methods for valuing path-dependent options using interpolation

Review of Derivatives Research

Volumn 5, Issue 3, 2002, Pages 273-314

  Forsyth, P A ^a   Vetzal, K R ^a   Zvan, R ^b  

^a UNIVERSITY OF WATERLOO   (Canada)

^b Bear Stearns & Co Inc   (United States)

Author keywords

Convergance; Forward shooting grid; Interpolation; Option pricing; Path dependence

Indexed keywords

EID: 1842548311     PISSN: 13806645     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020823700228     Document Type: Article

References (24)

1. Andreasen, J. (1998). "The Pricing of Discretely Sampled Asian and Lookback Options: A Change of Numeraire Approach," Journal of Computational Finance 2 (Fall), 5-30.
2. Barraquand, J. and T. Pudet. (1996). "Pricing of American Path-Dependent Contingent Claims," Mathematical Finance 6, 17-51.
3. Boyle, P. P., M. Broadie, and P. Glasserman. (1997). "Monte Carlo Methods for Security Pricing," Journal of Economic Dynamics and Control 21, 1267-1321.
4. Chalasani, P., S. Jha, F. Egriboyun, and A. Varikooty. (1999). "A Refined Binomial Lattice for Pricing American Asian Options," Review of Derivatives Research 3, 85-105.
5. Cox, J. C., S. A. Ross, and M. Rubinstein. (1979). "Option Pricing: A Simplified Approach," Journal of Financial Economics 7, 229-263.
6. Davidson, M. (1999). A Modification of the FSG Method for Pricing Average Options. Moscow State University, Faculty of Computational Mathematics, Working Paper.
7. Dempster, M. A. H., J. P. Hutton, and D. G. Richards. (1998). "LP Valuation of Exotic American Options Exploiting Structure," Journal of Computational Finance 2 (Fall), 61-84.
8. d'Halluin, Y., P. A. Forsyth, K. R. Vetzal, and G. Labahn. (2001). "A Numerical PDE Approach for Pricing Callable Bonds," Applied Mathematical Finance 8, 49-77.
9. Forsyth, P. A., K. R. Vetzal, and R. Zvan. (1999). "A Finite Element Approach to the Pricing of Discrete Lookbacks with Stochastic Volatility," Applied Mathematical Finance 6, 87-106.
10. Heston S. and G. Zhou. (2000). "On the Rate of Convergence of Discrete-Time Contingent Claims," Mathematical Finance 10, 53-75.
11. Hull, J. and A. White. (1993). "Efficient Procedures for Valuing European and American Path Dependent Options," Journal of Derivatives 1 (Fall), 21-31.
12. Kreiss, H. O., V. Thomée, and O. Widlund. (1970). "Smoothing of Initial Data and Rates of Convergence for Parabolic Difference Equations," Communications on Pure and Applied Mathematics 23, 242-259.
13. Leisen, D. and M. Reimer. (1996). "Binomial Models for Option Valuation: Examining and Improving Convergence," Applied Mathematical Finance 3, 319-356.
14. Li, A., P. Ritchken, and L. Sankarasubramanian. (1995). "Lattice Models for Pricing American Interest Rate Claims," Journal of Finance 50, 719-737.
15. Rannacher, R. (1984). "Finite Element Solution of Diffusion Problems with Irregular Data," Numerische Mathematik 43, 309-327.
16. Ritchken, P. and I. Chuang. (1999). "Interest Rate Option Pricing with Volatility Humps," Review of Derivatives Research 3, 237-262.
17. Ritchken, P., L. Sankarasubramanian, and A. M. Vijh. (1993). "The Valuation of Path Dependent Contracts on the Average," Management Science 39, 1202-1213.
18. Ritchken, P. and R. Trevor. (1999). "Pricing Options Under Generalized GARCH and Stochastic Volatility Processes," Journal of Finance 54, 377-402.
19. Wahlbin, L. B. (1980). "A Remark on Parabolic Smoothing and the Finite Element Method," SIAM Journal on Numerical Analysis 17, 33-38.
20. Wilmott, P. (1998). Derivatives. West Sussex, England: Wiley.
21. Wilmott, P., J. Dewynne, and S. Howison. (1993). Option Pricing: Mathematical Models and Computation. Oxford: Oxford Financial Press.
22. Windcliff, H., K. R. Vetzal, P. A. Forsyth, A. Verma, and T. F. Coleman. (2000). "An Object-Oriented Framework for Valuing Shout Options on High-Performance Computer Architectures," Journal of Economic Dynamcis and Control, forthcoming.
23. Zvan, R., P. A. Forsyth, and K. R. Vetzal. (1998). "Robust Numerical Methods for PDE Models of Asian Options," Journal of Computational Finance 1 (Winter), 39-78.
24. Zvan, R., P. A. Forsyth, and K. R. Vetzal. (1999). "Discrete Asian Barrier Options," Journal of Computational Finance 3 (Fall), 41-67.