| 美式期权执行日趋于无穷大的渐近分析及计算 |
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| 引用本文： | 边保军,代晓亮,袁桂秋.美式期权执行日趋于无穷大的渐近分析及计算[J].同济大学学报(自然科学版),2005,33(4):545-549. |
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| 作者姓名： | 边保军 代晓亮 袁桂秋 |
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| 作者单位： | 1. 同济大学,应用数学系,上海,200092
2. 杭州商学院,统计学院,浙江,杭州,310000 |
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| 基金项目： | 国家自然科学基金资助项目(10371088,10171078) |
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| 摘 要： | 讨论美式期权价格及最佳实施边界在执行日期趋于无穷大时的渐近性态.在相应的基本假设下,美式期权的定价模型是一个抛物型偏微分方程自由边界问题,而永久美式期权的定价模型是一个常微分方程自由边界问题.利用抛物型偏微分方程的渐近估计,证明美式期权价格及最佳实施边界收敛于永久美式期权价格及最佳实施边界,同时得到误差估计.数值计算的结果验证了上述结论.
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| 关 键 词： | 美式期权 抛物型偏微分方程 永久美式期权 执行日期 收敛性 误差估计 |
| 文章编号： | 0253-374X(2005)04-0545-05 |
Asymptotic Analysis and Numerical Computation of American Option When Expiry Date Runs to Infinity |
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| BIAN Bao-jun,DAI Xiao-liang,YUAN Gui-qiu.Asymptotic Analysis and Numerical Computation of American Option When Expiry Date Runs to Infinity[J].Journal of Tongji University(Natural Science),2005,33(4):545-549. |
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| Authors: | BIAN Bao-jun DAI Xiao-liang YUAN Gui-qiu |
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| Institution: | BIAN Bao-jun1,DAI Xiao-liang1,YUAN Gui-qiu2 |
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| Abstract: | We study the asymptotic behavior for price and optimal exercise boundary of American option when the expiry date goes to infinity.The models of American option and perpetual American option are a free boundary problem of parabolic partial differential equation and ordinary differential equation respectively.By using the asymptotic estimate,we prove that the price and optimal exercise boundary of American option converge to those of perpetual American option when the expiry date goes to infinity.Additionaly the error estimate is obtained.Also the numerical results verify and strengthen our conclusion. |
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| Keywords: | American option parabolic partial differential equation perpetual American option expiry date convergence error estimate |
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