随机流动性、资产交交换策略和定价研究

发布时间：2018-01-02 07:35

本文关键词：随机流动性、资产交交换策略和定价研究　出处：《华中科技大学》2013年博士论文　论文类型：学位论文

【摘要】：“流动性是市场的一切”,最近十几年一些重大金融事件的爆发让人们更加关注流动性和流动性风险,并从金融数学角度对其进行建模分析。流动性风险的引入会涉及到需要修正许多经典金融理论,包括资产配置、定价和风险管理。与其它流动性风险研究的相关文献不同,本文从流动性的随机性角度入手分别研究了资产交易和定价、对冲等相关问题,并重点讨论了随机性流动性所引发的新话题。具体地,本文分如下几个方面对其分别展开了研究：本文首先介绍了研究背景,并从实际现象中总结出一些流动性风险的主要特征,为整个论文建模提供实践依据。由于流动性风险并不像信用风险、市场风险那样被广大学者进行了深入研究,后二者的研究方法和结论都已标准化,但流动性风险连统一的定义都还存在争议,甚至不存在定性的概念。因此,本文在第二章首先归纳总结了目前主要文献对其定义和度量方法。紧接着,基于此结论本文在指令驱动交易制度下建立了综合的流动性模型,即包含了公认的流动性四要素：及时性、紧度、深度、反弹性。这不仅是更加现实的合理的流动性建模方法,而且在一定程度上拓展了市场微观结构理论,另外该模型也是整个论文的核心基础。随机流动性的引入使得相关最优化问题变得更复杂,并不能像传统模型那样可以得到最优交易策略的显性解。本文在期望流动性成本最小化下得到拟变分不等式,然后利用最优值函数的线性性进行降维,使用比率界限结构求解最优交易策略和无价格操纵的条件。然而当考虑均值方差形式的最小化问题时,最优值函数不存在线性性,本文使用一般随机最优控制方法得到了最优值函数是拟变分不等式的唯一粘性解。与具有深远意义的Cetin et al.(2004)不同,本文重点考虑了流动性的市场深度和及时性两个维度,在此框架下,流动性风险即使在连续有界变差交易策略下也不能被忽略。由于同时考虑随机流动性和波动,以及交易策略的限制,传统的完全对冲方法将失效,本文研究了这些扩展的上复制定价和对冲。在极端假设下,模型结论与B-S公式一致,因此,本研究的模型可以看成是传统模型的扩展。最后本文将前面的综合流动性模型和MMDH模型相融合,再使用随机加总的中心极限定理得到了资产收益率的极限分布,从中可以看到它的条件方差由流动性过程和信息到达过程组成。接下来首先使用校准方法检验了流动性对资产波动的影响,参数估计结果和拟合优度都具有很高的合理性。接着又假设具体随机过程得到两因素SV模型,选用EMM估计方法分别估计了传统单因素SV模型和两因素SV模型,发现前者被显著拒绝,而后者具有合理性,从估计参数可以看出,含流动性的两因素SV模型更能够拟合资产价格中的持久性和厚尾性。
[Abstract]:"liquidity is everything in the market", and the recent more than ten years of major financial events have made people pay more attention to liquidity and liquidity risk. The introduction of liquidity risk will involve the need to revise many classical financial theories, including asset allocation. Pricing and risk management. Different from other liquidity risk research literature, this paper studies asset trading, pricing, hedging and other related issues from the perspective of liquidity randomness. And it focuses on the new topic caused by randomness liquidity. Specifically, this paper has carried out the research on it in the following aspects: This paper first introduces the research background, and summarizes some main characteristics of liquidity risk from the actual phenomenon, which provides practical basis for the whole paper modeling. Because liquidity risk is not like credit risk, market risk has been deeply studied by scholars. The latter two research methods and conclusions have been standardized. However, even the unified definition of liquidity risk is still controversial, even there is no qualitative concept. Therefore, in the second chapter, this paper first summarizes the main literature on its definition and measurement methods. Based on this conclusion, this paper establishes a comprehensive liquidity model under the order-driven trading system, that is, includes the recognized liquidity of four elements: timeliness, tightness, depth. This is not only a more realistic and reasonable liquidity modeling method, but also extends the market microstructure theory to a certain extent, and it is also the core foundation of the whole paper. The introduction of stochastic liquidity makes the related optimization problems more complicated. The explicit solution of the optimal trading strategy can not be obtained as the traditional model. In this paper, the quasi-variational inequality is obtained under the minimization of the expected liquidity cost, and then the dimension is reduced by using the linearity of the optimal value function. The ratio bound structure is used to solve the optimal trading strategy and price manipulation conditions. However, when the mean variance minimization problem is considered, the optimal value function does not have linearity. In this paper, we obtain that the optimal function is the unique viscous solution of the quasi variational inequality by using the general stochastic optimal control method. Different from the far-reaching significance of Cetin et al. 2004, this paper focuses on the market depth and timeliness of liquidity, under this framework. Liquidity risk can not be ignored even under the continuous bounded variation trading strategy. Due to the consideration of random liquidity and volatility, as well as the restrictions of trading strategy, the traditional complete hedging method will be ineffective. In this paper, we study the upper-replication pricing and hedging of these extensions. Under extreme assumptions, the conclusion of the model is consistent with B-S formula. Therefore, the model of this study can be regarded as an extension of the traditional model. Finally, this paper combines the previous comprehensive liquidity model and MMDH model, and then uses random plus total central limit theorem to obtain the limit distribution of asset return. We can see that its conditional variance is composed of liquidity process and information arrival process. Then we use calibration method to test the influence of liquidity on asset volatility. The parameter estimation results and the goodness of fit are highly reasonable. Then the two factor SV model is obtained by assuming the specific stochastic process. The traditional single factor SV model and two factor SV model are estimated by using EMM estimation method. It is found that the former is significantly rejected, while the latter is reasonable, which can be seen from the estimation parameters. The two factor SV model with liquidity can better fit the persistence and thick tail of asset price.
【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：F224;F830.9

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