Research On Binomial Tree Method Of Interest Rate Option Pricing Under Vasicek Model

Interest rate options will be commissioning in China in 2020,the kind of product will help deepen the RMB interest rate marketization,so it has certain research value.We mainly consider the Vasicek interest rate model in terms of the selection of interest rate variable models on which the value of interest rate option depends.Vasicek interest rate model is a simple structure stochastic interest rate model,commonly used to describe the reality,and other more complex interest rate models can be regarded as the extension of this model.In this paper,we mainly use the binomial tree method of option pricing to study the pricing of interest rate options under the Vasicek stochastic interest rate model,which provides theoretical support for the value of interest rate options.The main research includes the following several aspects:Firstly,we study the binomial tree model and the option binomial tree model of Vasicek interest rate.We take interest rate as the underlying asset in this paper,based on the construction of the tree model,we assume three conditions to obtain the three parameters needed for the binomial tree movement mode,and we obtain two groups of parameter combinations finally.After comprehensive comparison,we use one group of parameters to construct the interest rate binomial tree model and the option binomial tree model,in which the option construction process takes the zero-coupon bond as the interest rate carrier.Secondly,we prove the convergence of the binomial tree model.In order to ensure the effective value of the interest rate option binomial tree,we will prove its convergence.Because the binomial tree model is a discrete model,we can't directly prove its properties,by proving the equivalence of the explicit difference scheme of interest rate option model and the pricing equation of option binomial tree model.Then we can directly obtain the convergence of option binomial tree model according to the equivalence,stability and related theorems.Then,we explore two deformations of the binomial tree model to ensure the applicability of the interest rate binomial tree model.We transform the binomial tree model respectively based on the?t infinitesimal principle and the regime-switching model and obtain two new interest rate binomial tree models,then we confirm the advantages and disadvantages of several interest rate binomial tree models by numerical simulation.Finally,the matrix form of interest rate option binomial tree is constructed.We summarize these option binomial tree models and obtain two types:the nodes respective are i+1 and 2~i at moment i,and then their matrix form can be deduced respectively.We study the numerical solution of option pricing by the matrix,it is shown that these two matrix forms are not limited to the situation of this paper,and other similar binomial tree models can also be applied directly.