挂钩黄金理财产品定价的数值方法

华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (5): 25-32.

挂钩黄金理财产品定价的数值方法

甄莉君, 张兴永, 牛成虎, 黎伟

中国矿业大学理学院, 徐州 221116

收稿日期:2011-01-01 修回日期:2011-04-01 出版日期:2011-09-25 发布日期:2011-11-22

Numerical method of financial product pricing linked to gold

ZHEN Li-jun, ZHANG Xing-yong, NIU Cheng-hu, LI Wei

College of Sciences, China University of Mining and Technology, Xuzhou 221116, China

Received:2011-01-01 Revised:2011-04-01 Online:2011-09-25 Published:2011-11-22

摘要/Abstract

摘要： 针对一款与黄金价格挂钩并具有双障碍期权性质的存款理财产品的定价问题, 引进改进的Crank-Nicolson计算方法得到它的数值解, 并通过Matlab编程验证了这种方法的可行性.通过与算子半群理论下的帕德逼近方法相结合, 不仅很好地处理了Crank-Nicolson方法在障碍点附近发散问题, 而且保留了该方法的精度高和稳定性强的优势. 在此基础上, 讨论了不同的市场波动率、收益利率和无风险利率对产品价值的影响. 数值算例表明, 该方法与实际情况吻合较好.

关键词: 理财产品, 数值解法, 双障碍期权, Crank-Nicolson方法, 帕德逼近

Abstract: For the problem of price a financial product linked to the gold pricing which has the property of double barrier options，this article provided an improved Crank-Nicolson calculation method to get the numerical solution, then verified the feasibility of this method via Matlab.This method, combined with the Pade schemes in the theory of semigroup operators, not only handled the problems of divergent near the obstacles spots, but also retained the strong advantages of high precision and stability of the Crank-Nicolson method. On this basis, the paper discussed the influence of the price of the product with different market volatility, interest rates and the risk-free rate. Finally, the numerical examples indicate that this method coincides the actual situation well.

Key words: financial product, numerical solution, double barrier options, Crank-Nicolson method, Pade schemes

中图分类号:

O211

甄莉君, 张兴永, 牛成虎, 黎伟. 挂钩黄金理财产品定价的数值方法[J]. 华东师范大学学报(自然科学版), 2011, 2011(5): 25-32.

ZHEN Li-jun, ZHANG Xing-yong, NIU Cheng-hu, LI Wei. Numerical method of financial product pricing linked to gold[J]. Journal of East China Normal University(Natural Sc, 2011, 2011(5): 25-32.

参考文献

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