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论文编号：	10139
作者编号：	1120140813
上传时间：	2018/6/9 17:30:25
中文题目：	基于Skew随机利率模型的定价研究及实证检验
英文题目：	Pricing Research and Empirical Test Based on the Skew-extended Stochastic Interest Rate Models
指导老师：	王永进
中文关键字：	Skew过程；随机利率模型；二叉树；三叉树；短期利率市场
英文关键字：	Skew process; stochastic interest rate model; binomial tree; trinomial tree; short rate market
中文摘要：	利率是宏观经济最重要的指标之一，利率问题是金融市场的一个基本问题，对利率的研究无疑有着非常重要的意义。从国际经验和国内实践来看，利率市场化是商品经济和自由市场发展的必然选择，但是，市场化的利率动态仍然可能存在明显的受控、受管制的特征，比如2008年金融危机后发达国家零利率和负利率现象的盛行、我国利率市场化进程中人民银行发挥利率决定的主导作用等。传统的随机利率模型在建模这种受控利率动态时遇到了挑战，基于此，本文提出了基于skew过程的随机利率模型。在该模型下，当利率运行到预先设定的skew水平时，会以预先确定的skew概率向上运动，这种特殊而有趣的性质使得其非常适合刻画具有受控特征的利率动态。因此，从实证角度检验该模型在拟合受控利率动态中的适用性，以及从理论角度实现该模型下的利率产品定价成为本文的主要研究内容。 在定价研究部分，本文使用网格方法，较为系统地研究了三大类基于skew过程的随机利率模型的债券与期权定价。对具有不连续漂移项的skew Vasicek模型，本文设计了跳幅度不统一的分段二叉树、分段三叉树定价方法，以匹配分段变换后过程波动率的不一致性；对skew CIR模型和双skew CIR模型，本文提出了统一的三叉树定价框架，可以仅通过调整跳概率来同时适应两种skew模型；对skew CEV模型，根据波动率弹性系数的三种情况，本文分别构造了存在多重跳的分段二叉树，以减少网格数量，提高定价效率。数值模拟表明这三种定价方法是高效且令人满意的，同时也揭示了基于skew模型的债券与期权价格许多有趣的特点，如skew模型价格相对于传统模型价格的偏离关系。 在实证检验部分，基于贝叶斯估计方法，本文将skew Vasicek模型应用到中国短期利率市场，对2007-2017年SHIBOR、银行间同业拆借利率、银行间质押式回购利率的四种到期期限数据动态特征进行拟合与检验。实证发现，隔夜与7天期限的所有市场skew模型均非常显著，且都存在隐含压力水平，1个月与3个月期限有一半市场skew模型显著。此外，对长期skew模型不显著的市场，在中期或短期区间上skew现象仍是普遍存在的。在预测方面，skew模型也比传统模型表现更优，再次验证了中国短期利率市场上skew模型的有效性。 全文共分七章，除引言与结论两章外，其余章节分别包括文献综述、基于skew Vasicek模型的债券与期权网格定价、基于skew CIR模型的债券与期权三叉树定价、基于skew CEV模型的债券与期权二叉树定价、基于skew Vasicek模型的中国短期利率市场实证。
英文摘要：	Interest rates are one of the most important macroeconomic indicators, and the interest rate problem is a basic problem for financial markets. Undoubtedly, the research of interest rate is of great importance. From the perspectives of international and domestic experience, interest rate liberalization is the inevitable choice of commodity economy and free markets. However, the market-determined interest rate may have controlled or regulated characteristics, for example, the prevailing zero or negative interest rate environments in developed countries after the 2008 financial crisis; the leading role of People's Bank of China in the process of interest rate liberalization. The traditional stochastic interest rate models are challenged when modeling the regulated interest rate dynamics, therefore, this dissertation proposes the skew-extended stochastic interest rate models. Under the specification of such skew-extended models, the interest rate will move upwards with pre-determined skew probability once it touches the pre-specified skew level. This special path property of skew process makes it very suitable for capturing interest rate dynamics in regulated markets. As a result, our research mainly focuses on: empirically examining the feasibility of skew process in fitting regulated interest rate dynamics, and theoretically resolving the interest rate derivative pricing problems under such skew-extended models. In the pricing part of this dissertation, we use lattice approaches to value bonds and options under the assumption that short rate follows three classes of skew-extended stochastic interest rate models. For the generalized skew Vasicek model with discontinuous drift coefficient, we design a nonuniform jump size piecewise binomial tree and piecewise trinomial tree to match the nonuniform volatility of the piecewise transformed process. For the skew CIR model and the doubly skewed CIR model, we propose a uniform framework of trinomial tree method, such that it can accommodate both skew-extended CIR models by only adjusting the jump probabilities. For the skew CEV model, we construct a piecewise binomial tree with multiple jumps in three situations of the volatility elasticity parameter, the setting of multiple jumps can reduce the number of branches to improve efficiency. Numerical simulations not only demonstrate that our lattice approaches are efficient and satisfactory, but also reveal many interesting bond and option price features of skew-extended models, for example, the price deviation effect due to the skew local time component. In the empirical part of this dissertation, by using Bayesian estimation method, we estimate and test the skew Vasicek model in Chinese short rate market. The data include overnight, 7-day, 1-month and 3-month short rates for Shanghai Interbank Offered Rate (SHIBOR), China Interbank Offered Rate (CHIBOR) and Chinese Interbank Pledged Repo Rate, covering the period from January 2007 to December 2017. We find that the skew Vasicek model is significant for all of the overnight and 7-day markets, and for half of the 1-month and 3-month market, in which there exists implicit resistance level. Besides, even if the skew-extended model is not significant in the long-run for some markets, the skew phenomenon can be commonly observed in the short- and mid-run. Furthermore, the skew-extended model performs better than the traditional model in predicting the future, attesting to the effectiveness of the skew process in Chinese short rate market. This dissertation is composed of seven chapters. In addition to two chapters of the introduction and conclusion, the remaining chapters include literature review, lattice approach for the generalized skew Vasicek model with discontinuous drift, trinomial trees for the skew-extended CIR models, binomial trees for the skew CEV model, an empirical research of skew Vasicek model on Chinese short rate market.
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