券商集合理财产品的定价研究

发布时间：2018-01-31 03:09

本文关键词： 非完备市场效用无差别保底条款非系统风险契约设计　出处：《湖南大学》2013年硕士论文　论文类型：学位论文

【摘要】：券商集合理财产品已经成为我国金融理财市场中不可忽视的重要力量，本文运用效用无差别原理对券商集合理财产品进行定价研究。在非完备市场和投资者风险厌恶假设下，结合最优投资策略，利用随机控制原理，得出HJB方程，再根据效用无差别原理，推导出产品价格满足的偏微分方程，并用差分法对价格方程进行数值求解。结果表明：当风险厌恶系数足够大时，产品效用无差别价格随着封闭期延长反而降低且；风险态度仅通过产品的非系统风险影响产品价格，若产品与市场相关性越弱，非系统风险越大，风险态度对价格影响越大，反之亦然，若完全相关，非系统风险为零，风险态度不对价格产生影响；产品价格与固定管理费率和超额收费率呈非线性关系。本文还精确地求解出了产品的系统风险溢价和非系统风险溢价，并从风险溢价的角度解释了价格随着产品价格随着产品波动率增大反而降低这一与B-S公式反常的结论，最后，根据固定管理费和超额收费之间的权衡关系，从效用无差别的角度讨论了产品的契约设计问题。文章的主要内容包括以下几个方面：首先，先讨论了券商集合理财产品的契约特性，得出了投资者的收益公式，在完备市场假设下，投资者根据金融市场中三种资产进行财富配置，投资者以终止时刻财富期望最大化为目标，选择最优投资策略，，根据效用无差别原理，运用随机控制方法，推导出了产品效用无差别满足的偏微分方程，并根据券商集合产品的契约，得出相应的边界条件。其次，讨论了非完备市场下券商集合理财产品的定价问题，因为券商集合理财产品是不可交易的资产且产品管理者必须持有一部分基金份额，致使产品有不可对冲的非系统风险；同样地，根据效用无差别原理，推导出了产品效用无差别价格满足的偏微分方程。最后，根据价值方程，运用有限差分方法，进行相关经济分析，并从效用无差别的角度讨论了产品的契约设计问题。
[Abstract]:Based on the principle of non - complete market and investor ' s risk aversion , it is concluded that the price of product is less than that of B - S formula . Firstly , the paper discusses the contract characteristics of the wealth management products of the securities trader , and obtains the investors ' income formula . Under the assumption of complete market , the investor chooses the optimal investment strategy according to the three kinds of assets in the financial market , and chooses the optimal investment strategy . According to the principle of non - difference of utility , the partial differential equation satisfying the difference of product utility is derived , and the corresponding boundary condition is obtained according to the contract of the product of the securities trader . Secondly , we discuss the pricing problem of the financial products of the securities traders under the imperfect market , because the financial products of the securities firms are non - tradable assets and the product managers have to hold a part of the fund shares , so that the products have non - systematic risks which are not hedged . Similarly , according to the principle of utility indifference , the partial differential equations which are satisfied by the difference price of the utility of the products are derived . Finally , according to the value equation , the related economic analysis is carried out by using the finite difference method , and the contract design of the product is discussed from the point of difference of utility .

【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.5;F224

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