| 美式利率期权定价的抛物型变分不等式 |
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| 引用本文： | 高长林,易法槐. 美式利率期权定价的抛物型变分不等式[J]. 高校应用数学学报(A辑), 2008, 23(1): 13-22 |
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| 作者姓名： | 高长林 易法槐 |
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| 作者单位： | 广东金融学院应用数学系,广东广州,510521;华南师范大学教学科学学院,广东广州,510631 |
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| 基金项目： | 国家自然科学基金(10671075)，广东省自然科学基金(5005930)，高等学校博士点基金(20060574002) |
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| 摘 要： | 应用PDE方法对美式利率期权定价问题进行理论分析.在CIR利率模型下美式利率期权定价问题可归结为一个退化的一维抛物型变分不等式.通过引入惩罚函数证明了该变分不等式的解的存在唯一性,然后研究了自由边界的一些性质,如单调性,光滑性和自由边界在终止期的位置.
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| 关 键 词： | 利率期权 期权定价 变分不等式 自由边界 |
| 文章编号： | 1000-4424(2008)01-0013-10 |
| 修稿时间： | 2007-01-26 |
A parabolic variational inequality arising from the valuation of American interest rate options |
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| GAO Chang-lin,YI Fa-huai. A parabolic variational inequality arising from the valuation of American interest rate options[J]. Applied Mathematics A Journal of Chinese Universities, 2008, 23(1): 13-22 |
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| Authors: | GAO Chang-lin YI Fa-huai |
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| Abstract: | The valuation of American interest rate options is analyzed theoretically using a PDE method.Under the assumption that interest rate obeys the CIR model,the valuation of American interest rate options can be formulated as a one-dimensional degenerate parabolic variational inequality. The existence and uniqueness of the solution of the variational inequality are proved using a penalty function.Some properties of the free boundary are studied,such as monotonicity,smoothness and the location of the free boundary at expiry. |
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| Keywords: | interest rate option option pricing variational inequality free boundary |
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