体制转换下等价鞅测度的构造研究

发布时间：2018-08-22 15:11

【摘要】：体制转换资产价格模型可以描述宏观经济的影响,但在金融衍生产品定价所涉及的等价鞅测度的构造问题中,利用传统的Esscher变换方法得到的等价鞅测度实质上只考虑了微观市场风险,而没有考虑体制转换所表示的宏观经济风险.此外,经典的几何布朗运动不能刻画资产收益率的尖峰厚尾现象.本文首先利用马尔科夫过程和最大化非广延熵分布建立了一个新的资产价格模型.该模型可以同时描述体制转换和尖峰厚尾现象.然后利用鞅理论,借助微观市场的资产价格过程和宏观经济的马尔科夫过程的乘积给出了一种新的等价鞅测度构造方法,通过该方法构造的等价鞅测度包含了微观市场和宏观经济两种风险.最后,在该等价鞅测度下,给出了资产价格折现过程为鞅的充要条件,为进一步研究金融衍生产品的定价及风险控制提供了理论基础.
[Abstract]:The asset price model of institutional transformation can describe the macroeconomic influence, but in the construction of equivalent martingale measure involved in the pricing of financial derivatives, The equivalent martingale measure obtained by using the traditional Esscher transformation method in essence only considers the micro market risk but not the macroeconomic risk represented by the system transformation. In addition, the classical geometric Brownian motion can not describe the sharp and thick tail phenomenon of asset return. In this paper, a new asset price model is established by means of Markov process and maximization of nonexpansive entropy distribution. The model can describe both the system transition and the peak thick tail phenomenon. Then a new equivalent martingale measure construction method is given by using martingale theory and the product of the asset price process and the Markov process in the micro market. The equivalent martingale measure constructed by this method includes two kinds of risks: micro market and macro economy. Finally, under the equivalent martingale measure, the necessary and sufficient conditions for the asset price discounting process to be martingale are given, which provides a theoretical basis for further study on the pricing and risk control of financial derivatives.
【作者单位】：上海理工大学管理学院;皖西学院金融与数学学院;皖西学院金融风险智能控制与预警研究中心;
【基金】：国家自然科学基金(11171221) 上海市一流学科(系统科学)项目(XTKX2012) 安徽省高校优秀青年基金(2012SQRL196) 安徽高校省级优秀青年基金重点项目(2013SQRL071ZD)~~
【分类号】：F830.9;F224

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