A fast high-order finite difference algorithm for pricing American options

Journal of Computational and Applied Mathematics

Volumn 222, Issue 1, 2008, Pages 17-29

  Tangman, D Y ^a   Gopaul, A ^a   Bhuruth, M ^a  

^a UNIVERSITY OF MAURITIUS   (Mauritius)

Author keywords

American options; Finite difference method; Free boundary; High order compact scheme; Singularity separating

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; FINITE DIFFERENCE METHOD; FLOW PATTERNS; INITIAL VALUE PROBLEMS; NUMBER THEORY; NUMERICAL ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS;

AMERICAN OPTIONS; BLACK-SCHOLES EQUATIONS; BLACK-SCHOLES PDE; COMPACT SCHEMES; EFFICIENT IMPLEMENTATION; FINITE-DIFFERENCE ALGORITHMS; FREE BOUNDARIES; FREE BOUNDARY; FREE BOUNDARY VALUE PROBLEMS; HIGH-ORDER; HIGH-ORDER COMPACT SCHEME; HIGH-ORDER FINITE DIFFERENCES; LOCATION BASED; NON-UNIFORM GRIDS; NUMERICAL EXPERIMENTS; NUMERICAL SOLUTIONS; SINGULARITY SEPARATING; SMOOTH PASTING CONDITION; TRI-DIAGONAL SOLVER;

NUMERICAL METHODS;

EID: 52949105812     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2007.10.044     Document Type: Article

References (23)

1. Achdou Y., and Pironneau O. Computational Methods for Option Pricing. SIAM (2005), Frontiers in Applied Mathematics, Philadelphia
2. Borici A., and Lüthi H. Pricing American Options by Fast Solutions of the Linear Complementarity Problem. In: Kontoghiorghes E., Rustem B., and Siokos S. (Eds). Computational Methods in Decision-Making, Economics and Finance (2002) 325-338
3. Borici A., and Lüthi H. Fast solutions of complementarity formulations in American put pricing. J. Comput. Fin. 9 1 (2005)
4. Brennan M., and Schwartz E. The valuation of American put options. J. Fin. 32 2 (1977) 449-462
5. X. Chen, J. Chadam, R. Stamicar, The optimal exercise boundary for American put options: Analytic and numerical approximations. Preprint, 2000
6. Dempster M.A.H., Hutton J.P., and Richards D.G. LP valuation of exotic American options exploiting structure. J. Comput. Fin. 2 (1998) 61-84
7. Forsyth P.A., and Vetzal K.R. Quadratic convergence of a penalty method for valuing American options. SIAM J. Sci. Comput. 23 6 (2002) 2096-2123
8. Goodman J., and Ostrov D.N. On the early exercise boundary of the American put option. SIAM J. Appl. Math. 62 5 (2002) 1823-1835
9. Han H., and Wu X. A fast numerical method for the Black-Scholes equation of American options. SIAM J. Numer. Anal. 41 6 (2003) 2081-2095
10. Heston S., and Zhou G. On the rate of convergence of discrete-time contingent claims. Math. Fin. 10 (2000) 53-75
11. Ikonen S., and Toivanen J. Operator splitting methods for American option pricing. Appl. Math. Lett. 17 (2004) 809-814
12. Jaillet P., Lamberton D., and Lapeyere B. Variational inequalities and the pricing of American options. Acta Appl. Math. 21 (1990) 263-289
13. Kangro R., and Nicolaides R. Far field boundary conditions for Black-Scholes equations. SIAM J. Numer. Anal. 38 4 (2000) 1357-1368
14. Kim I.J. The analytic valuation of American options. Rev. Fin. Stud. 3 4 (1990) 547-572
15. Leisen D., and Reimer M. Binomial models for option valuation-examining and improving convergence. Appl. Math. Fin. 3 (1996) 319-346
16. Nielsen B.F., Skavhaug O., and Tveito A. Penalty and front-fixing methods for the numerical solution of American option problems. J. Comput. Fin. 5 (2002) 69-97
17. Samuelson P.A. Rational theory of warrant pricing. Ind. Manage. Rev. 6 (1965) 13-32
18. Smith R. Optimal and near-optimal advection-diffusion finite-difference schemes. Part 2: Unsteadiness and non-uniform grid. Proc. Roy. Soc. Lond. 456 (2000) 489-502
19. Tavella D., and Randall C. Pricing Financial Instruments: The Finite Difference Method (2000), John Wiley and Sons, New York
20. Wilmott P., Howison S., and Dewynne J. The Mathematics of Financial Derivatives (1995), Cambridge University Press, New York
21. Wu L., and Kwok Y.K. A front-fixing finite difference method for the valuation of American options. J. Fin. Eng. 6 2 (1997) 83-97
22. Y.L. Zhu, H. Ren, H. Xu, Improved effectiveness evaluating American options by the singularity-separating method, Working paper, University of North Carolina of Charlotte, Charlotte, 1996
23. Zhu Y.L., Wu X., and Chern I.L. Derivatives Securities and Difference Methods (2004), Springer, New York