Analysis Of The Daily Interval Interest-Bearing Bonds Based On Interest Rate Model

This paper mainly analyzes the interval interest-bearing bonds linked to interest rate index based on the theory of stochastic differential equations.First of all,we select the daily single-range interest bonds linked to 3MLIBOR interest rates as the analysis object.For a given range of pre-designed interest [a,b],based on the sample data of 3MLIBOR interest rate,we assume that the index rate was satisfied with the time homogeneous diffusion process of the Dothan model.Then,we can apply the maximum likelihood method to estimate the parameters.With the estimated parameters,this paper uses the relevant theories of time homogeneous diffusion process of the first time interval,and gives the time expected theoretical value of first arrival interval [a,b] boundary of the time homogeneous diffusion process after the parameter estimation,and Monte Carlo simulation results of the desired value estimate of the first time.The results shows that the Monte Carlo simulation can be used to estimate the theoretical value well.We take a further application of Monte Carlo simulation and obtains the numerical estimation of total time expectation of the interest rate diffusion process falling in the area from a to b in a certain period of time.At the same time,the Monte Carlo simulation is carried out under a more general assumption that the interest rate index was consistent with the CIR model.Secondly,based on the theory of martingale method and the assumption that the interest rate index satisfies the Dothan interest rate model,this paper gives the pricing process linked to the interest rate index of the two value option.We take the daily interval interest bonds as the sum of risk-free zero-coupon bonds and daily observation interval binary options,then give the pricing formulas of daily single interval and double interval interest bearing bonds respectively.For the daily double interval interest bearing bonds,we first consider pricing under the situation that the two types of interest rates are independent,and expand the pricing analysis to relevant interest rate indicators.This paper discusses the interval interest-bearing bonds from different angles,and provides a reference for investors who take an interest in these new bond varieties.