Pricing Bond Type Bank Financial Product With Wishart Model

Structured financial products are popular in the financial marke of the western developed countries, its main principle is that structured products = fixed income +floating income + options.Structured financial products satisfies the basic demand of risk and return of the investors under the condition of the market risk which is difficult to predict, it also has more flexibility,and it is a personalized investment tool.So since the nineties in last century, it becames popular in the western investors.And we can also see, personalized design of structured financial products has a good adaptability for the uncertainty of the financial market risk, so the structural bank financial products will be a good deal in the future, especially after the complete marketization of interest rate in our country.This is also the significance of this article research.In this paper, based on the basic construction of structured financial products in the west,We design a bond type products for the domestic interbank market,it invests to the two types of structural interval bonds(does not contain options trading).Range accrual bond is a kind of structural bonds, interest rates range accrual debt will pay higher interest rates referring to the market when on the due time the interest rate falls into a certain setted interval, or the current pay is zero.This paper designed type A bond type bank financial products,which is to invest the fixed income range accrual bond,type B bond bank financial products invest floating income range accrual bonds.The pricing model is two-dimensional Wishart model and another model is the two-dimensional CIR model embedded in a two-dimensional Wishart model.Wishart process is a matrix form of stochastic differential process, the model parameters and state variables are multidimensional matrix, this paper discuss only two-dimensional matrix.In the process of pricing,the Wishart process moment generating function form is an important link of operation.In the concrete computational expressions the Fourier transform and fast Fourier transform are used.Model parameter estimation is a difficult point of this article.We does not use markov chain monte carlo simulation(MCMC), but the higher precision of extended kalman filter(EKF) method for simulating Wishart matrix parameters in the model, then we can estimate the state variables x of the Wishart process and then to estimate the short-term interest rate r, which can calculate the price of bonds.In this paper, the data sample is the yield to maturity on the fixed rate bonds between our country bank data from 2007 to 2014,a total of 768 sample data.The aboveis the second, third,and the fourth general train thought and research methods.Another important content of this article is to draw the bank financial products curve and to do a comparative analysis,because this article for pricing analysis uses Wishart Term Structure Model( WTSM) and Two- dimensional Cox- Ingersol- Ross Model(TCIR).The main changes of the latter is that the diagonal line elements of state variables x are changed into a one-dimensional CIR process, because a one-dimensional Wishart model and a one-dimensional CIR model has the same structure, so in this paper,we study the two-dimensional Wishart model and TCIR model, and at the same time pricing bond with the two models.In addition, before specific pricing, this paper sets the range accrual bond interest rate range and the conditions of different maturity structure.Comparing from three aspects,first is to compare two types of bank financial products A and B, second is to compare different maturities of the bond type bank financial products, third is to compare difference of the two models and to give the analysis of the reasons for the difference.Finally, there are so many places to expand about the Wishart model in the field of financial instruments pricing research, this paper study can give some reference to the future researchers.