摘要
随着20世纪70年代布雷顿森林体系瓦解等一系列重大事件的出现,利率、汇率的市场化使得金融市场越来越复杂多变。特别是近几年来,中国在利率市场化和现代金融市场的建设上的步伐越来越大,衍生品市场建设步入了关键时期。由此引发的衍生品定价问题成为目前金融理论研究和实践研究的热点之一。
本文在动态利率期限结构研究的基础上,对金融市场中的以利率、国债以及商品为标的的衍生工具的定价问题进行深入研究。在整个研究的过程中,本文始终与中国的实际经济环境密切联系,从实用的角度出发来研究中国市场环境下的衍生品定价问题。全文从五个方面对此进行研究:
首先,本文对比分析了NS模型和SNS模型对中国国债市场利率期限结构的适用性问题,发现NS与SNS模型均适合中国的债券市场,但从整体上来看,NS模型优于SNS模型。为此,进一步将横截面的NS模型推广到时间序列上,通过对NS模型中瞬时远期利率的各组成部分与主要宏观经济因素如工业产值增长率、广义货币增长率、通货膨胀率和银行间拆借当月加权平均利率之间关系的分析,揭示利率各部分的成因及与经济因素之间的内在关系。本文还从NS模型角度检验了中国债券市场的纯预期假说,研究结果表明该假说在中国国债市场上具有很高的显著性。虽然这种显著性是中国利率市场化现状的产物,但我们认为这并不能说明中国债券市场是“有效的”。
其次,在前一章获得利率期限结构的时间序列基础上,通过分析中国的宏观经济因素与国债收益率之间的关系,本文建立符合中国债券市场的动态利率期限结构模型。该模型融合了定义良好的宏观经济变量的动态过程,并采用Kalman滤子对模型进行估计,所得结果表明该模型能够很好地拟合中国债券市场的收益率曲线。我们把债券收益率中包含宏观经济变量的风险溢价进行分解,研究结果部分解释了长期债券收益率大于中短期债券收益率的原因,也揭示了中国债券市场较国外特别是美国债券市场收益率偏低的原因。本文进一步研究了包含有宏观经济因素的动态利率期限结构所隐含的货币政策,讨论了实际利率、货币政策市场化的目标利率、实际利率预期和均衡实际利率的关系,为货币政策的正确实施提供了理论上的依据。
第三,引入随机动态的宏观经济变量,建立动态利率期限结构模型,采用Kalman滤波对模型参数进行估计。在此基础上,推导包含实际利率和通货膨胀因素的仿射期限结构下的利率互换、利率期权(利率上/下限、利率双限)等与利率有关的衍生品的价格,并对上述利率衍生工具价格的数值解进行讨论。研究发现,对于固定利率-浮动利率互换协议的价格来说,利率互换与一般的金融衍生品相类似,具有明显的时间价值。此外,结合Feynman-Kac定理,采用特征函数的傅立叶逆变换方法,对各种常见的利率衍生产品的价格进行研究,并给出了利率上限期权价的数值解。
第四,进一步讨论考虑宏观变量仿射期限结构的债券衍生工具定价研究问题。在等价鞅框架下,采用傅立叶变换的方法计算贴现国债期权、贴现国债期货期权、贴现国债期货、息票债券及其期货等与利率有关的衍生品的价格,并在参数估计上,给出各种债券衍生工具具体的数值解;
最后,基于商品期货价格决定理论,建立了随机利率、现货价格和潜在过程三因素的随机模型,并在等价鞅测度下,推导出期货价格所遵循的常微分方程组;同时,采用特征函数Fourier逆变换的方法对商品期权的定价进行了研究,最后,采用大连商品交易所大豆期货交易数据及现货价格,结合Kalman滤波和Runge-Kutta方法估计出模型的参数,进而求得商品期货以及商品期权价格的数值解。通过研究,本文得到以下结论:利率过程和现货价格过程具有明显的均值回复特征,模型能很好地拟合期货市场的价格序列;通过对理论定价和真实价格的比较发现,这两个价格的偏差在可接受的范围内,模型可以对真实市场中期货价格的定价效率进行评价,投资者可以通过模型计算寻找高估或低估的期货合约。
As the disorganization of the Bretton Woods System in the 1970’s, many momentous events occurred. The financial market became more and more complex because of the mercerization of interest rate and exchange rate. Recently, China made bigger steps in mercerization of interest rate and construction of the modern financial market and it becomes more and more urgent to establish a comprehensive derivatives market. For these reasons, the pricing of derivatives is one of the important issues in the researches of the modern financial theories and practices.
In this dissertation, we will discuss the pricing issues of the derivatives on interest rate, national bonds and commodities under the fundamental researches on dynamic interest rate term structures. We establish connections between the problems of pricing of derivatives and the real economical elements in China. The main contents of the dissertation are as follows:
Firstly, we compare interest rate term structures of Chinese bond market fitted by NS model and SNS model using the time serial of national bonds’prices, we find that both NS model and SNS model are suitable to build the interest rate term structure, but NS model is better than SNS model. We also analyzed the three components of the instantaneous future interest rate through the macro-economic variables like industry production rate, M2, inflation rate and inter-bank interest rates, etc. to reveal the causes of interest rate. While testing the Pure Expectation Hypothesis over NS model, we find that the probability of the acceptance of PEH is extremely high. But this highly prominence is the outcome of the actuality of mercerization interest rate in China rather than the effective bond market in China. The PEH of NS model can be applied to the forecast of the term structure of interest rates.
Secondly, we establish a well-defined dynamic model that combines the inflation, real interest rate and their central tendencies by the results of analyzing the relations between the macro-economic variables and bond yields. Base on the results of Kalman filter, we decompose the risk premium of the yield curve which partly explains the reason that the yield of long-term bond is larger than the yield of short-term bonds; the risk premium can also explain why yields in Chinese bond market are lower than those in U.S. bond market. We also analyze the implied monetary policy above the dynamic model. The results reveal significance for the implementation of monetary policies, investment activities and pricing of the financial derivatives.
Thirdly, we introduce macro-economic variables to establish a dynamics model. Base on the parameters estimation results of Kalman filter, we deduce pricing formula about interest rate swap and interest rate options. Just like other financial derivatives, a fixed-floating interest rate swap contract has its time values. We also adopt Feynman-Kac theory and the Fourier inversion of the conditional characteristic function to calculate the numerical price of interest rate options (interest rate floor, interest rate cap and interest rate collar). Detail numeric analysis is discussed in this section.
Fourthly, as a further step of the pricings of interest rate derivatives, we discuss the pricings of bond derivatives. Under an equivalent martingale framework, we deduce the pricing formula about discount bond option, discount bond futures, discount bond futures option, coupon bond, coupon bond option, etc. those whose prices derive from the interest rate level. Numerical calculations are shown in the section.
Lastly, futures market is very important to investors and hedgers, prices discovery is one of its basic functions. According to the theory of storage, we characterize a three-factor model of commodity spot prices, convenience yields, and interest rates processes. The model allows convenience yields to depend on spot prices and interest rates. It also allows for time varying risk premium. We deduce the futures price equation under equivalent martingale. Adopting the soybean futures-spot prices serials; we estimate the parameters and solve the ODEs by Kalman filter and Runge-Kutta. We also discuss the commodity option price by Fourier inversion numerically. We apply the results in forecasting and evaluate the futures price; the errors show that our model can capture the dynamics of the futures price.
引文
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