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Convergence property of an interior penalty approach to pricing American option
1. | Department of Finance, Business School, Shenzhen University, Nanhai Ave 3688, Shenzhen, Guangdong 518060 |
2. | School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009 |
References:
[1] |
A. Bensoussan and J. L. Lions, "Applications of Variational Inequalities in Stochastic Control," North-Holland, Amsterdam-New York-Oxford, 1982. |
[2] |
F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Political Economy, 81 (1973), 637-659.
doi: 10.1086/260062. |
[3] |
M. Brennan and E. Schwartz, The valuation of American put options, J. Finance, 32 (1977), 449-462.
doi: 10.2307/2326779. |
[4] |
J. C. Cox, S. A. Ross and M. Rubinstein, Option pricing: A simplified approach, J. Financial Econom., 7 (1979), 229-263.
doi: 10.1016/0304-405X(79)90015-1. |
[5] |
G. Dauvaut and L. J. Lions, "Inequalities in Mechanics and Physics," Springer-Verlag, Berlin-Heidelberg-New York, 1976. |
[6] |
M. A. H. Dempster, J. P. Hutton and D. G. Richards, LP valuation of exotic American options exploiting structure, J. Comp. Fin., 2 (1998), 61-84. |
[7] |
E. M. Elliot and J. R. Ockendon, "Weak and Variational Methods for Moving Boundary Problems," Pitman, 1982. |
[8] |
P. A. Forsyth and K. R. Vetzal, Quadratic convergence for valuing American options using a penalty method, SIAM J. on Sci. Comput., 23 (2002), 2095-2122.
doi: 10.1137/S1064827500382324. |
[9] |
R. Glowinski, "Numerical Methods for Nonlinear Variational Problems," Springer-Verlag, New York, 1984. |
[10] |
J. Haslinger, M. Miettinen and D. P. Panagiotopoulos, "Finite Element Method for Hemivariational Inequalities: Theory, Methods and Applications," Kluwer Academic Publishers, Dordrecht, 1999. |
[11] |
J. Huang and J.-S. Pang, Option pricing and linear complementarity, J. Comp. Fin., 2 (1998), 31-60. |
[12] |
A. Q. M. Khaliq, D. A. Voss and S. H. K. Kazmi, A linearly implicit predictor-corrector scheme for pricing American options using a penalty method approach, J. Banking Finance, 30 (2006), 489-502.
doi: 10.1016/j.jbankfin.2005.04.017. |
[13] |
B. F. Nielsen, O. Skavhaug and A. Tveito, Penalty and front-fixing methods for the numerical solution of American option problems, J. Comp. Fin., 5 (2001), 69-97. |
[14] |
B. F. Nielsen, O. Skavhaug and A. Tveito, Penalty methods for the numerical solution of American multi-asset option problems, J. Comput. Appl. Math., 222 (2008), 3-16.
doi: 10.1016/j.cam.2007.10.041. |
[15] |
S. Wang, X. Q. Yang and K. L. Teo, Power penalty method for a linear complementarity problem arising from American option valuation, J. Optim. Theory Appl., 129 (2006), 227-254.
doi: 10.1007/s10957-006-9062-3. |
[16] |
P. Wilmott, J. Dewynne and S. Howison, "Option Pricing: Mathematical Models and Computation," Oxford Financial Press, Oxford, 1994. |
[17] |
K. Zhang, S. Wang, X. Q. Yang and K. L. Teo, A power penalty approach to numerical solution of two-factor American option pricing, Numer. Math: TMA, 2 (2009), 202-223. |
[18] |
K. Zhang, X. Q. Yang and K. L. Teo, A power penalty approach to American option pricing with jump diffusion processes, JIMO, 4 (2008), 767-782. |
[19] |
R. Zvan, P. A. Forsyth and K. R. Vetzal, Penalty methods for American options with stochastic volatility, J. Comput. Appl. Math., 91 (1998), 199-218.
doi: 10.1016/S0377-0427(98)00037-5. |
show all references
References:
[1] |
A. Bensoussan and J. L. Lions, "Applications of Variational Inequalities in Stochastic Control," North-Holland, Amsterdam-New York-Oxford, 1982. |
[2] |
F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Political Economy, 81 (1973), 637-659.
doi: 10.1086/260062. |
[3] |
M. Brennan and E. Schwartz, The valuation of American put options, J. Finance, 32 (1977), 449-462.
doi: 10.2307/2326779. |
[4] |
J. C. Cox, S. A. Ross and M. Rubinstein, Option pricing: A simplified approach, J. Financial Econom., 7 (1979), 229-263.
doi: 10.1016/0304-405X(79)90015-1. |
[5] |
G. Dauvaut and L. J. Lions, "Inequalities in Mechanics and Physics," Springer-Verlag, Berlin-Heidelberg-New York, 1976. |
[6] |
M. A. H. Dempster, J. P. Hutton and D. G. Richards, LP valuation of exotic American options exploiting structure, J. Comp. Fin., 2 (1998), 61-84. |
[7] |
E. M. Elliot and J. R. Ockendon, "Weak and Variational Methods for Moving Boundary Problems," Pitman, 1982. |
[8] |
P. A. Forsyth and K. R. Vetzal, Quadratic convergence for valuing American options using a penalty method, SIAM J. on Sci. Comput., 23 (2002), 2095-2122.
doi: 10.1137/S1064827500382324. |
[9] |
R. Glowinski, "Numerical Methods for Nonlinear Variational Problems," Springer-Verlag, New York, 1984. |
[10] |
J. Haslinger, M. Miettinen and D. P. Panagiotopoulos, "Finite Element Method for Hemivariational Inequalities: Theory, Methods and Applications," Kluwer Academic Publishers, Dordrecht, 1999. |
[11] |
J. Huang and J.-S. Pang, Option pricing and linear complementarity, J. Comp. Fin., 2 (1998), 31-60. |
[12] |
A. Q. M. Khaliq, D. A. Voss and S. H. K. Kazmi, A linearly implicit predictor-corrector scheme for pricing American options using a penalty method approach, J. Banking Finance, 30 (2006), 489-502.
doi: 10.1016/j.jbankfin.2005.04.017. |
[13] |
B. F. Nielsen, O. Skavhaug and A. Tveito, Penalty and front-fixing methods for the numerical solution of American option problems, J. Comp. Fin., 5 (2001), 69-97. |
[14] |
B. F. Nielsen, O. Skavhaug and A. Tveito, Penalty methods for the numerical solution of American multi-asset option problems, J. Comput. Appl. Math., 222 (2008), 3-16.
doi: 10.1016/j.cam.2007.10.041. |
[15] |
S. Wang, X. Q. Yang and K. L. Teo, Power penalty method for a linear complementarity problem arising from American option valuation, J. Optim. Theory Appl., 129 (2006), 227-254.
doi: 10.1007/s10957-006-9062-3. |
[16] |
P. Wilmott, J. Dewynne and S. Howison, "Option Pricing: Mathematical Models and Computation," Oxford Financial Press, Oxford, 1994. |
[17] |
K. Zhang, S. Wang, X. Q. Yang and K. L. Teo, A power penalty approach to numerical solution of two-factor American option pricing, Numer. Math: TMA, 2 (2009), 202-223. |
[18] |
K. Zhang, X. Q. Yang and K. L. Teo, A power penalty approach to American option pricing with jump diffusion processes, JIMO, 4 (2008), 767-782. |
[19] |
R. Zvan, P. A. Forsyth and K. R. Vetzal, Penalty methods for American options with stochastic volatility, J. Comput. Appl. Math., 91 (1998), 199-218.
doi: 10.1016/S0377-0427(98)00037-5. |
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