时变波动率模型下到期区间理财产品定价问题
Pricing of Financial Products in Maturity Interval under Time-Varying Volatility Model
摘要:
本文在时变波动率Black-Scholes模型下，研究了到期区间理财产品的定价问题。首先，利用偏微分方程方法得到了金融理财产品的定价公式。接着，利用二次变差方法提取积分波动率，再选取四种理财产品进行实证分析，并对其选择给出建议。最后，为投资者选择金融理财产品提供了一系列的参考建议。
Abstract:
In this paper, we study the pricing of maturity interval financial products under the Black-Scholes model of time-varying volatility. First, the pricing formula of financial wealth management products is obtained by using the partial differential equation method. Then, the quadratic variation method is used to extract the integral volatility, and then four wealth management products are selected for empirical analysis, and suggestions are given for their selection. Finally, it provides a series of reference suggestions for investors to choose financial wealth management products.
参考文献
|
[1]
|
周海林, 吴鑫育, 高凌云, 等. 随机利率条件下的欧式期权定价[J]. 系统工程理论与实践, 2011, 31(4): 729-734.
|
|
[2]
|
张茂军, 秦学志, 南江霞. 基于三角直觉模糊数的欧式期权二叉树定价模型[J]. 系统工程理论与实践, 2013, 33(1): 34-40.
|
|
[3]
|
孙玉东, 师义民, 童红. 基于摄动理论的障碍期权定价[J]. 应用数学学报, 2015, 38(1): 67-79.
|
|
[4]
|
孙玉东, 王秀芬, 童红. 非线性Black-Scholes模型下障碍期权定[J]. 系统科学与数学, 2016, 36(4): 513-527.
|
|
[5]
|
董艳. 非线性Black-Scholes模型下Bala期权定价[J]. 高校应用数学学报, 2016, 31(1): 9-20.
|
|
[6]
|
姜礼尚. 期权定价的数学模型和方法[M]. 第2版. 北京: 高等教育出版社, 2008.
|
|
[7]
|
Polyanin, A.D. (2002) Handbook of Linear Partial Differential Equations for Engineers and Scientists. Chapman & Hall/CRC, Boca Raton.
|
|
[8]
|
孙玉东. 随机过程及其应用[M]. 西安: 西北工业大学出版社, 2016.
|
|
[9]
|
张世英. 金融时间序列分析[M]. 北京: 清华大学出版社, 2008.
|
|
[10]
|
张波, 余超, 毕涛. 高频金融数据建模理论、方法与应用[M]. 北京: 清华大学出版社, 2015.
|