Study On Pricing Callable Bond Of Commercial Banks In China

The bond market of China starts relatively late.There is a certain gap between the bond market of China and that of developed countries.The difference is reflected in size,variety and structure.However,compared to the past of our country,the expansion speed of the scale of bond issuance is accelerated and the types of the products are more abundant,so it is necessary to increase the research and analysis towards the bonds in Chinese bond market.On one hand,the research methods of how to pricing callable and puttable bonds are depend on foreign research more,and domestic research is insufficient.On the other hand,the case analysis of the domestic bond market is very limited.Which data is used for pricing bond is a very important part and the kind of products and the level of interest rate are different between domestic market and foreign market.It is very important to use actual data rely on domestic financial products when we pricing bonds of China,so speeding up the research on the domestic interest rate products is necessary and form our country's own system.In order to study how to price callable and puttable bonds,we must study the short-term interest rate models first.In general,the short-term interest rate models were mainly divided into single factor models,double factor models and multi factor models.From the angle of application,the single factor model is more concise,so we mainly introduce the single factor model in this paper.Equilibrium models in the short-term interest rates are the earliest models,using historical data to estimate the parameters is suitable,but the common flaw of these model is that they can not match the initial term structure of interest rates.Thus,based on equilibrium models,no arbitrage models began to develop,and no arbitrage models are more suitable for bond pricing,so we adopt these models in practice.Callable bond or puttable bond is a kind of embedded option bonds.There are a lot of different methods to price callable bond and puttable bond.The first method is considering separating the bond and option.The theoretical price of the callable bond is equal to the price of common bond minus the price of redemption right.The theoretical price of puttable bond is equal to the price of common bond plus the price of resale right.For the option pricing part,using the option pricing formula can price European bond option,and the trinomial tree(Hull-White model)method or more complex method as finite difference method is available to price American bond option.The second method to price these bonds is the tree method.Many financing institution use binary tree(BDT model)method to do the pricing job.But the interest rate of the binary tree is divergent,it does not accord with the character of mean reversion of interest rates.By contrast,trigeminal tree(Hull-White model)is more consistent with the actual situation,but it may appear negative interest rates in the trigeminal tree.By referring to the foreign paper,a large number of empirical test shows that negative interest rates can be revised to zero.Because such revision have little impact to the pricing of bond,and after that,the rate is more consistent with the actual situation.The third one is using Monte Carlo simulation method to simulate the short rate.Under this method,the path of rate is more abundant.However,the number of simulation paths must reach a certain amount in order to ensure the accuracy of the pricing,always leading to a long running time.In this paper,we mainly adopt the trinomial tree(Hull-White model)method to price callable bond and puttable bond.The first step of this work is how to estimate the parameters in this model.The parameters needed to be estimated in the Hull-White model has the same meaning of these parameters in Vasicek model and parameters in Vasicek model can be estimated through historical data,so we mainly study how to estimate the parameters of Vasicek model.According to Pan Guanzhong's essay(2004),there are two criteria to select which rate is more suitable to estimate the parameters in single factor model of interest rate.He proved the first criteria which has been proposed that the change of interest rate must have highest correlation with other short-term interest rates' change is right and suggested the second principle is that choosing those the rate which is traded the most frequently and whose trading volume is the most.The inter-bank repo rate of seven days(R007)is the best replacement to the instantaneous interest rate.Most of the previous essay focused on the callable bond and puttable bond which are issued by China Development Bank in the case analysis part.Because the commercial banks also takes a great proportion in callable and puttable bonds issuers,and most of those bonds which are issued by commercial banks are subordinated bonds,so this paper focuses on the case analysis of Commercial Bank Subordinated callable bonds.It is similar to the puttable bonds.In this paper,we use a simple parameter estimation method which is called the least squares estimation.We tested the method is effective in pricing callable bonds,and in the next time we can try more complex parameter estimation methods such as generalized method of moments(GMM),maximum likelihood estimation and nonparametric estimation methods.At the end of this article,we carried out a sensitivity analysis of these two parameters.By comparing the results,discovered that option callable bonds which is embedded with American option is very sensitive to parameter,so estimating parameter well is an important work,and parameter estimation is accurate or not will affect the quality of the pricing.