| 拟蒙特卡罗法在亚洲期权定价中的应用 |
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| 引用本文： | 詹惠蓉,程乾生.拟蒙特卡罗法在亚洲期权定价中的应用[J].数学的实践与认识,2005,35(9):20-27. |
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| 作者姓名： | 詹惠蓉 程乾生 |
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| 作者单位： | 北京大学数学科学学院,北京,100871 |
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| 摘 要： | 亚洲期权是场外交易中几种最受欢迎的新型期权之一,但它的价格却没有解析表达式,到目前为止,亚洲期权的定价仍是个公开问题.本文采用拟蒙特卡罗法中的Halton序列来估计它的价格,数值结果表明当观察点的个数N13时,它比蒙特卡罗法要好.本文还利用MATLAB程序生成了随机Halton序列,并将它与控制变量法结合起来估计亚洲期权的价格,估计值标准差的比较表明它在大多情况下比相应的蒙特卡罗法的估计效果要好.
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| 关 键 词： | 亚洲期权 拟蒙特卡罗法 蒙特卡罗法 控制变量 |
| 修稿时间： | 2003年3月15日 |
Quasi-Monte Carlo methods for Pricing Asian Options |
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| ZHAN Hui-rong,CHENG Qian-sheng.Quasi-Monte Carlo methods for Pricing Asian Options[J].Mathematics in Practice and Theory,2005,35(9):20-27. |
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| Authors: | ZHAN Hui-rong CHENG Qian-sheng |
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| Abstract: | Asian options are one of the most popular exotic options in OTC markets, but there is no closed form solution for its price yet. To date, pricing Asian optons is still an open problem. This paper adopt one of low-discrepancy sequence, Halton sequence, to evaluate the price. Numerical results show that it is better than its counterpart Monte Carlo estimator when the number of observation is less than 14. The randomized Halton seqence, generated by MATLAB program, combined with different control variates are also studied to estimate the price. Numerical results show that they consistently do better jobs than their counterpart Monte Carlo control variates estimators when N is 5. |
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| Keywords: | Asian options Monte Carlo methods quasi-Monte Carlo methods control variates |
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