The Petrov-Galerkin Method For Pricing Of Bond Of Options

In recent decades, with the development of the financial market and continuous improvement and maturation of the modern financial theory, a large variety of financial derivatives have been designed, which have formed a market and exerted significant influence on global economy.Options, especially, became the most active one in the financial derivative market, have a rapid development and wide application since the nineties. This is because it has the excellent functions of avoiding risk, risk investment and value identification, and demonstrates the characteristics of flexibility and diversity. Options are the core instrument for risk management. Options Theory is one of the greatest discoveries of twenty century. Black, Scholes and Merton put forward core formula of option pricing, therefore won the Nobel economics prize in 1997.The researches on Options mainly focus on two fields:One is how to construct new and pragmatic options to meet the demands of continues varied market investment; the other one is how to certain the value of Options based on the different assumptions, in other words, it is the problem of Options pricing, which also is the focus of mathematics research.In the Black-Scholes modle, the assumption that interest rate is constant or deciding function is accepted equivalence to the short-time options or assets of stocks. But to the derivation stock, this is unaccepted assumption. This way of calculating the price of options that apply Black-Scholes resulted in discrepancy between the option price and real price. In order to calculate more accurately the price of derivative bonds based on interest rates, we must conduct research on subject of random interest.This thesis is to build a pricing model of bonds and options under the ECIR model through the process of constructive demonstrate and demonstrate the existence and unique of solution, and promote the results to the multi-factor model, which is base on the term structure of interest rates proposed by Cox-Ingerson-Ross (1985), i.e. ECIR model and YANG(2006)'s calibration method, then calculates encountered integral-differential equation through applying method of Petrov-Galerkin and Block-by-block, and calculate and analyze the price of the kind of bond options. At last, the thesis gives the examples of demonstration and analyzes and discusses the outcome of these examples.