Pricing American options with uncertain volatility through stochastic linear complementarity models

Computational Optimization and Applications

Volumn 50, Issue 2, 2011, Pages 263-286

  Hamatani, Kenji ^a   Fukushima, Masao ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

American option; Option pricing; Stochastic linear complementarity problem; Uncertain volatility

Indexed keywords

AMERICAN OPTIONS; COMPLEMENTARITY PROBLEMS; EXPECTED RESIDUAL MINIMIZATION; EXPECTED VALUES; LINEAR COMPLEMENTARITY; NUMERICAL RESULTS; OPTION PRICING; STOCHASTIC LINEAR COMPLEMENTARITY PROBLEM; SUFFICIENT CONDITIONS; UNCERTAIN VOLATILITY;

ECONOMICS; STOCHASTIC SYSTEMS;

STOCHASTIC MODELS;

EID: 80054958066     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-010-9344-4     Document Type: Article

References (23)

1. G. Bakshi C. Cao Z. Chen 1997 Empirical performance of alternative option pricing models J. Finance 52 2003 2049 10.2307/2329472 (Pubitemid 127344421)
2. Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming. Springer, New York (1997)
3. F. Black M. Sholes 1973 The pricing of options and corporate liabilities J. Polit. Econ. 4 637 654 10.1086/260062
4. P. Boyle P. Phelim 1977 Options: A Monte Carlo approach J. Finance Econ. 4 323 338 10.1016/0304-405X(77)90005-8
5. M.J. Brennan E.S. Schwartz 1977 The valuation of American put option J. Finance 32 449 462 10.2307/2326779
6. X. Chen M. Fukushima 2004 Expected residual minimization method for stochastic linear complementarity problems Math. Oper. Res. 30 1022 1038 2185828 10.1287/moor.1050.0160 (Pubitemid 43134189)
7. X. Chen C. Zhang M. Fukushima 2009 Robust solution of monotone stochastic linear complementarity problems Math. Program. 117 51 80 2421299 1165.90012 10.1007/s10107-007-0163-z
8. N. Clark K. Parrott 1999 Multigrid for American option pricing with stochastic volatility Appl. Math. Finance 6 177 195 10.1080/135048699334528
9. Cottle, R.W., Pang, J.S., Stone, R.E.: The Linear Complementarity Problem. Academic Press, San Diego (1992)
10. J.C. Cox S.A. Ross M. Rubinstein 1979 Option pricing: A simplified approach J. Finance Econ. 7 229 268 1131.91333 10.1016/0304-405X(79)90015-1
11. S.P. Dirkse M.C. Ferris 1995 The PATH solver: A non-monotone stabilization for mixed complementarity problems Optim. Methods Softw. 5 123 156 10.1080/10556789508805606
12. Facchinei, F., Pang, J.S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, I and II. Springer, New York (2003)
13. G. Gurkan A.Y. Ozge S.M. Robinson 1999 Sample-path solution of stochastic variational inequalities Math. Program. 84 313 333 1690005 10.1007/ s101070050024
14. Hamatani, K., Fukushima, M.: Pricing American options with uncertain volatility through stochastic linear complementarity models. Technical Report 2010-004, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University (2010)
15. S.L. Heston 1993 A closed form solution for options with stochastic volatility with applications to bond and currency options Rev. Financ. Stud. 6 327 343 10.1093/rfs/6.2.327
16. J. Huang J.S. Pang 1998 Option pricing and linear complementarity J. Comput. Finance 2 31 60
17. Hull, J.C.: Options, Futures, and Other Derivatives. Prentice Hall, Upper Saddle River (2000)
18. Kall, P., Wallace, S.W.: Stochastic Programming. Wiley, New York (1994)
19. Marti, K.: Stochastic Optimization Methods. Springer, Berlin (2005)
20. Svensson, O., Vorobyov, S.: A subexponential algorithm for a subclass of P-matrix generalized linear complementarity problems. Technical Report, DIMACS (2005)
21. J.A. Telly 1994 Valuing American options in path simulation model Trans. Soc. Actuar. XLV 499 520
22. Wilmott, P., Dewynne, J.N., Howison, S.: The Mathematics of Financial Derivatives-A Student Introduction. Cambridge University Press, Cambridge (1995)
23. R. Zvan P.A. Forsyth K.R. Vetzal 1998 Penalty methods for American options with stochastic volatility J. Comput. Appl. Math. 91 119 218 1628686 10.1016/S0377-0427(98)00037-5