Interest Rate Derivatives Pricing Research

This paper studies the pricing of interest rate derivatives, modeling the three factors stochastic mean and stochastic volatility interest rate term structure with jump character, and pricing three interest rate derivatives which including convertible bonds, floating interest rate bonds and interest rate futures.This paper summarizes the development of theory and models of interest rate term structure, analyzes and resolves three difficult problems in term structure. They are the nonlinear of drift mean, the conditional heteroskedasticity of volatility and extreme interest rate because of paroxysmal events. The process of stochastic mean describes the nonlinear characters of interest rate drift process better than simple constant mean process. The conditional heteroskedasticity is described by GARCH model. Adding jump into pure diffusion process, considering the effects of paroxysmal events and the lag effect caused by historical events will overcome the limitation of traditional pure diffusion model incapable of forecast the jump behavior of interest rate accurately. This paper builds the stochastic mean and stochastic volatility interest rate term structure model, SVJ-SD model for short. In this paper, I choosing the repo interest rate of national debt of China as sample, making empirical research of SVJ-SD model and its five special instances CIR, CKLS, CT, SV and SV-SD models, using maximum likelihood method to estimate CIR, CKLS and CT models, and using efficient method of moment to estimate SV, SV-SD and SVJ-SD models because they contain latent variables and their likelihood functions didn't got easily. The efficient method of moment avoids the limited sample characteristic in virtue of semi-nonparametric model. Comparing the virtue and shortcoming of the six interest rate term structure models in their estimate process, parameter results and forecast effect.This paper analyzes the structure and the items of convertible bond. It is one kind of mixed bond including convertible option, resell option,callable option.The convertible option isn't the ordinary European call option, but an American exchange option. And the three kinds of options have the characters of exclusive and coexistence when they are not executed. I clean up the developing course of convertible pricing from structured pricing system and contracted pricing system, and build the two-factors dynamic interest rate convertible bonds pricing method. I deduce the general differential equation and boundary conditions of pricing convertible bonds from It? lemma. I build dynamic interest rate binominal tree and the stock pricing binominal tree of convertible bond. And put forward a method of combining the interest rate tree and stock price tree innovatively. I use month tree and half a year tree to price the convertible bond of China Commercial Bank, and analyze coupon and convertible likelihood of it, and summarize the convertible bond development course of our country.The vital step of determining the coupon rate of floating interest rate bonds is to determine benchmark interest rate and benchmark interest rate spread. For benchmark rate, the highly developed marketable interest rate such as LIBOR has been chosen. As to benchmark interest rate spread, many factors shall been taken into consideration such as the adjustment of the relationship between fixed interest rate and floating interest rate, tax, and bond credit. In the pricing of floating interest rate bonds, the key point lies in the term structure of interest rate that determines the cash discount rate. Choosing future rate derived from SVJ-SD the term structure of interest rate as benchmark interest rate, employing binominal tree instrument, floating interest rate bonds which contain no option or contain interest rate floor and cap and interest rate collar. It's suggested that floating interest rate bonds be introduced, the benchmark interest rate should be determined according to int'l standard, also new product should be developed. To meet with the demands of new product developing, a floating interest rate bond related to stock returns is created which can serve as financing product in insurance industry. The uncertainty of stock returns is similar with the benchmark interest rate stochastic pattern. Some stock returns can be treated as bonds' benchmark interest rate. Three situations are discussed and pricing is done in accordance with the three situations respectively.The interest rate future agreement is an efficient hedging financial instrument, of which agreement forward rate is a flexible in curb exchange. The value of agreement forward rate depends on fixed future rate as well as dynamics structure of interest rate. National debt future is the routine interest rate derivative. Foreign normalized approaches could be referred in the pricing of middle term and long-term national debt future. After regulating the conversion factor parameter to determine the received cash price of short of the future. The short may complete the transaction by choosing the cheapest bond. The theory of no arbitrage can assure the price short-term national debt future equals the value of bond par value discounted by future interest. The time and economic conditions to introduce national debt future again have been mature. The introducing of national debt future step by step represents the imminent demand of various marketing institutions to hedging interest rate risk.