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| 倒向随机微分方程与巴黎期权的非线性定价 | |
| 引用本文： | 郭冬梅,宋斌,汪寿阳. 倒向随机微分方程与巴黎期权的非线性定价[J]. 中国科学:数学, 2013, 43(1): 91-103. DOI: 10.1360/012012-426 |
| 作者姓名： | 郭冬梅 宋斌 汪寿阳 |
| 作者单位： | 中央财经大学经济学院, 北京100081; 中央财经大学管理科学与工程学院, 北京100081; 中国科学院数学与系统科学研究院, 北京100190 |
| 基金项目： | 教育部人文社会科学研究青年基金(批准号:11YJC790015);国家社会科学基金一般项目(批准号:11BJL018)资助项目 |
| 摘 要： | 巴黎期权是一种复杂的奇异期权. 本文基于倒向随机微分方程, 定义了巴黎期权的非线性价格过程, 分析其性质, 并且给出巴黎期权非线性定价的偏微分方程表达式. 在金融市场收益率不确定的情形以及存贷利率不同的情形下分别对连续巴黎期权进行定价和具体的数值分析, 结论显示巴黎期权的非线性定价机制更具合理性. |
| 关 键 词： | 倒向随机微分方程 巴黎期权 路径依赖 偏微分方程 |
Backward stochastic differential equations and nonlinear pricing Parisian(Parasian) options |
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| GUO DongMei,SONG Bin , WANG ShouYang. Backward stochastic differential equations and nonlinear pricing Parisian(Parasian) options[J]. Scientia Sinica Mathemation, 2013, 43(1): 91-103. DOI: 10.1360/012012-426 | |
| Authors: | GUO DongMei SONG Bin & WANG ShouYang |
| Affiliation: | GUO DongMei,SONG Bin & WANG ShouYang |
| Abstract: | Parisian (Parasian) options are complex exotic options. In this paper, we define the nonlinear Parisian (Parasian) options, and construct the pricing formula of partial differential equations based on the backward stochastic differential equations. We present two examples of imperfect market, one is that the expected return is uncertain, the other takes into account a higher interest rate for borrowing than for lending. Results show that the pricing mechanism of nonlinear Parisian (Parasian) is more reasonable. |
| Keywords: | backward stochastic differential equation Parisian options path dependent partial differential equation |
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