An Inverse Problem Of The Interest Rate Derivative Pricing

The financial model at different levels of management are an impor-tant method used to provide business solutions to the problem, a tool forformulate investment strategies . At present, the financial model in the fi-nancial and non-financial corporate governance has been widely applied.Through modeling the establishment of the financial model to determinethe currency swaps, interest rate changes, stock market risks and a widerrange of securities pricing model relations.The financial model is also usedto assess investment in securities prices, travel trade strategy, positioningthe risk of trade prediction. The financial model for a wide range of appli-cations, almost every securities firms in the course of business are basedon a financial model.Finance theory is the core of study with the risk premium related tothe present value of the currency. Securities are financial interests, such asstocks and bonds, the value keep continuing until the trade stop. On behalfof the company stock ownership, stock ownership of the people have theright to request access to the company's profits. Bonds are at a future timeon the protocol of the claim proceeds. In this paper, we focus on the bondpricing model.In economics,the value of one yuan in the future is less than today.The value of the future convert into the present value which is smaller,this the time value of money. However, in the real market, cash ?ow is uncertain ,the future payment is uncertain. There is the risk problem, andthen bring out the risk pricing problem to be discussed.The interest rates change means the change of the bond spot yieldcurve is uncertainty.It refers to changes in yield curve in a relatively shortperiod of time interval (such as one month) within the yield curve shapechanges.As all of the curve is from the yield curve consisting of principaland interest coupons separation, changes in yield curve must express allthe changes in bond prices, while changes in the prices of all bonds are notmutually independent, but related. In order to describe changes in yieldcurve, we will separate the changes in yield into two parts: the expec-tations of drift rate or expected rate of return ,and the uncertain change,real-time with the drift of interest rates and risk-related.For bond pricing equation, the problem is to get the bond prices , andthe inverse problem is that we have already known the bond's expectedmarket prices at a certain moment , the requirement is to determine themarket price of risk.In the previous scientific research, scholars have a similar financialmodel problem has been the anti-research, for example, VICTOR quadISAKOV's"The Inverse Problem Of Option Pricing", as well as GUAN-QUAN ZHANG and PEIJUN LI's"An quad Inverse Problem Of Deriva-tive Security Pricing". The later article is the basis of the thesis's im-provements."An Inverse Problem Of Derivative Security Pricing"is the interestrate risk pricing model to study the situation that the boundary conditionsis 0 , the risk is 0, so a lot of derivation of the process of calculationhave been simplified. However, in reality, not all the models satisfy theboundary conditions about the risk is 0. Cox-Ingersoll-Ross (CIR) model is based on the production processin economy, pricing process, the empirical foundation on an acceptablemodel of a bond. But it is also a risk of non-zero boundary conditions ofinterest rate models situation. For the inverse problem of the introductionof CIR model results, and make use of relevant equations for the CIRmodel the risk of market pricing, we need to risk boundary conditions ofnon-homogeneous case with a complete mathematical reasoning, as wellas numerical experiments to verify .This is also the focus of discussion inthis thesis.By analyzing the calculation,we get the adjoint equation of the non-homogeneous risk boundary conditions rate equationand a integration - differential Equation which contain the price ofriskλ(t)By discrete both of them, we can find out the price of the risk.Financial models use the formula so that you can use the data inputof securities prices, decide the pricing decision-making. At least in prin- ciple, can be described, namely, the financial model at the actual financialoperations can be executed and have direct significance. However, wehave to know the financial model's limitations of their uses, good or baddepends on whether it can produce an accurate enough prediction ,it mustbe based to determine their actual effectiveness.Reality, for the CIR-type single-factor (interest rate) model, the mar-ket price of risk has its constraints.Only to compare the model we built,that we can know the advantages and disadvantages of this method.Theprice constraints of the risk in our model among this thesis is:The interest pricing model is a guide for the activities which re-lated to the market,and pricing by inverse method is definitely a successfulmodel about the using of mathematics in finance.This idea is a solid the-oretical background and practical method with far-reaching significance.