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Convergence rate of free boundary of numerical scheme for American option
1. | Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260 |
2. | Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556 |
3. | Department of Mathematics, Tongji University, Shanghai 200092 |
4. | School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006 |
References:
[1] |
X. Chen and J. Chadam, A mathematical analysis of the optimal exercise boundary for American put options, SIAM Journal on Mathematical Analysis, 38 (2007), 1613-1641.
doi: 10.1137/S0036141003437708. |
[2] |
X. Chen, J. Chadam, L. Jiang and W. Zheng, Convexity of the exercise boundary of the American put option on a zero dividend asset, Mathematical Finance, 18 (2008), 185-197.
doi: 10.1111/j.1467-9965.2007.00328.x. |
[3] |
J. Cox and M. Rubinstein, Option pricing: A simplified approach, J. Finan. Econ., 7 (1979), 229-263. |
[4] |
A. Friedman, Variational Principles and Free Boundary Problems, John Wiley and Sons, New York, 1982. |
[5] |
Hall, J., Options, Futures, and Other Derivatives, Prentice-Hall, Inc., New Jersey, 1989. |
[6] |
B. Hu, L. Jiang and J. Liang, Optimal convergence rate of the explicit finite difference scheme for american options, J. Comp. Appl. Math., 230 (2009), 583-599.
doi: 10.1016/j.cam.2008.12.018. |
[7] |
L. Jiang, Mathematical Modeling and Methods for Option Pricing, World Scientific, 2005.
doi: 10.1142/5855. |
[8] |
L. Jiang and M. Dai, Convergence of the explicit difference scheme and the binomial tree method for American options, J. Comp. Math., 22 (2004), 371-380. |
[9] |
L. Jiang and M. Dai, Convergence of binomial tree methods for European/American options path-depedent options, SIAM J Numer. Anal., 42 (2004), 1094-1109.
doi: 10.1137/S0036142902414220. |
[10] |
J. Liang, B. Hu, L. Jiang and B. Bian, On the rate of convergence of the binomial tree scheme for American options, Numerische Mathematik, 107 (2007), 333-352.
doi: 10.1007/s00211-007-0091-0. |
[11] |
J. Liang, B. Hu and L. Jiang, Optimal convergence rate of the binomial tree scheme for American options with jump diffusion, SIAM Financial Mathematics, 1 (2010), 30-65.
doi: 10.1137/090746239. |
[12] |
R. Myneni, The pricing of the American option, The Annals of Applied Probability, 2 (1992), 1-23.
doi: 10.1214/aoap/1177005768. |
[13] |
X. Qian, C. Xu, L. Jiang and B. Bian, Convergence of the binomial tree method for American options in jump-diffusion model, SIAM J. Numer. Anal., 42 (2005), 1899-1913.
doi: 10.1137/S0036142902409744. |
[14] |
C. Xu, X. Qian and L. Jiang, Numerical analysis on binomial tree methods for a jump-diffusion model, J. Com. and Appl. Math. 156 (2003), 23-45.
doi: 10.1016/S0377-0427(02)00903-2. |
[15] |
W. Wilmott, S. Howison and J. Dewyne, The Mathematics of Financial Derivatives, Cambridge University Press, 1995.
doi: 10.1017/CBO9780511812545. |
show all references
References:
[1] |
X. Chen and J. Chadam, A mathematical analysis of the optimal exercise boundary for American put options, SIAM Journal on Mathematical Analysis, 38 (2007), 1613-1641.
doi: 10.1137/S0036141003437708. |
[2] |
X. Chen, J. Chadam, L. Jiang and W. Zheng, Convexity of the exercise boundary of the American put option on a zero dividend asset, Mathematical Finance, 18 (2008), 185-197.
doi: 10.1111/j.1467-9965.2007.00328.x. |
[3] |
J. Cox and M. Rubinstein, Option pricing: A simplified approach, J. Finan. Econ., 7 (1979), 229-263. |
[4] |
A. Friedman, Variational Principles and Free Boundary Problems, John Wiley and Sons, New York, 1982. |
[5] |
Hall, J., Options, Futures, and Other Derivatives, Prentice-Hall, Inc., New Jersey, 1989. |
[6] |
B. Hu, L. Jiang and J. Liang, Optimal convergence rate of the explicit finite difference scheme for american options, J. Comp. Appl. Math., 230 (2009), 583-599.
doi: 10.1016/j.cam.2008.12.018. |
[7] |
L. Jiang, Mathematical Modeling and Methods for Option Pricing, World Scientific, 2005.
doi: 10.1142/5855. |
[8] |
L. Jiang and M. Dai, Convergence of the explicit difference scheme and the binomial tree method for American options, J. Comp. Math., 22 (2004), 371-380. |
[9] |
L. Jiang and M. Dai, Convergence of binomial tree methods for European/American options path-depedent options, SIAM J Numer. Anal., 42 (2004), 1094-1109.
doi: 10.1137/S0036142902414220. |
[10] |
J. Liang, B. Hu, L. Jiang and B. Bian, On the rate of convergence of the binomial tree scheme for American options, Numerische Mathematik, 107 (2007), 333-352.
doi: 10.1007/s00211-007-0091-0. |
[11] |
J. Liang, B. Hu and L. Jiang, Optimal convergence rate of the binomial tree scheme for American options with jump diffusion, SIAM Financial Mathematics, 1 (2010), 30-65.
doi: 10.1137/090746239. |
[12] |
R. Myneni, The pricing of the American option, The Annals of Applied Probability, 2 (1992), 1-23.
doi: 10.1214/aoap/1177005768. |
[13] |
X. Qian, C. Xu, L. Jiang and B. Bian, Convergence of the binomial tree method for American options in jump-diffusion model, SIAM J. Numer. Anal., 42 (2005), 1899-1913.
doi: 10.1137/S0036142902409744. |
[14] |
C. Xu, X. Qian and L. Jiang, Numerical analysis on binomial tree methods for a jump-diffusion model, J. Com. and Appl. Math. 156 (2003), 23-45.
doi: 10.1016/S0377-0427(02)00903-2. |
[15] |
W. Wilmott, S. Howison and J. Dewyne, The Mathematics of Financial Derivatives, Cambridge University Press, 1995.
doi: 10.1017/CBO9780511812545. |
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