A Research On Yield Curve Of Inter-bank Bond Market Based On Dynamic Nelson-Siegel Model

It is increasingly significant for financial institution to make a research on term structure in accordance with the need of interest risk and asset management. Investor can get advice from yield curve and regulator can also benefit from it. Fitting and prediction is the core of term structure theory.Modern theory of term structure includes static model, no-arbitrage model, affine model, macro-finance model and hybrid model. Static model fits yield curve of a specific time-point, such as McCulloch(1971),Vasicek(1982) and Fama(1987). No-arbitrage model and affine model derives from stochastic processes. Relevant models are Vasicek model, CIR model and HJM model. Macro-finance model combines economic variables with yield curve. For example, Wu(2003) studied the effect of macro-finance impulse on term structure. Ang(2003) studied affine model with economic variable. Hybrid model aims to mix these models, such as Diebold (2002)(2006) proposed Dynamic Nelson-Siegel model. In China, Zhu (2003) and Yu (2010) both studied term structure of Shanghai exchange.Static model and dynamic model fit yield curve well, but their prediction result is no well in contrast with macro-finance model and hybrid model. In China, scholars fit and predict yield curve of inter-bank and exchange with macro-finance model and closing price. However, there is no research about yield curve using bid-ask price.This paper calculates the factors with dynamic Nelson-Siegel model and bid-ask price. Then we combine yield curve with macro-econometric data and it becomes a hybrid model. According to our testing, the prediction result and economic explanation are significant.There are six parts in this paper. Firstly, we introduce the background, mathematic tools, study procedures and innovations.In the second part, we write a literature review of term structure in history. We introduce classic theories and models of term structure, such as static model, dynamic model, hybrid model and macro-finance model. Studies in China are reviewed in different classification.In the third part, there is a conclusion of models and testing in this article. In the beginning, we introduce Nelson-Siegel model and three factors. Then there is a brief review of state space model and Kalman filter. Numeric method is important for solution, so quasi-Newton method is also introduced. At last, we come to recall time series models, such as VAR, VECM and Johansen co-integration testing.Fourth part is about how to collect and process data. We explain why we use bid-ask price in this article. Then we process the data and calculate spot rates with Fama-Bliss Bootstrapping method.Fifth part is the main part of this paper. We calculate three factors of Nelson-Siegel model and predict these factors with VAR. Then we proposed a co-integration function with economy theory and compare the new model with VAR in prediction.Last, we make some suggestion and make conclusions for this paper.From our study, we get some new thoughts. First, there is a co-integration function with level, slope, curvature, CPI and IP. Second, prediction is more accurate when macro-economy indexes are included in model.There are three innovations in this article. First, a new model with three factors and macro-economy variables is proposed. We find that the prediction results are better than unrestricted vector auto-regression model. Second, different from other yield curve of exchange, we fit yield curve of inter-bank bond market with bid-ask price. Third, we calculate initials of numeric maximization method to better fit dynamic Nelson-Siegel model.There are two study directions in the future. First, with try and error method, more macro-economy variables can be included in our model. Second, λ can become the fourth latent factor of state space model (Koopman,2010), so some improvement may be significant with time-varying λ.