Research About Option Pricing Under Stochastic Interest Rates Model

Stock option bargaining was carried out formally in Chicago Board Options Exchange after 1973. It is 31 years ever since then, now option market has become an important part of international finance market. But option market is still a theoretical and unpractical concept in China. However we believe that with the development of Chinese marketability process, option market will inevitably enter into Chinese economy domain. Finance technologies would make either a country's economy prosperous or finance crisis. In this sense, finance study should be part of country security and network technologies. So it's very necessary to study systemically option, which is an innovative finance core tool. Understanding across-the-board the meaning and characters of option not only has important theory value for mastering high-class finance technology, but also has profound practical significance for the cultivating and developing of option market in China.So evading risk in financial trading market cries for pricing options is an insistent need. Therefore, in this paper the general knowledge of option, research actuality and develop course of theory of option pricing was firstly presented; then on the base of the B-S's pricing formula of European option, we obtain European option pricing changing interest rates process are either diffusion process or Ito process and we introduce the contents, methods and results about the pricing theory of option. Assuming that it exists an equivalent martingale measure and there are two securities traded one of which is riskless and the other is risky in the efficiency market; and when interest rates process is a solution of a special equation, we gets pricing of American option; finally we will discuss the conditions of existence of an equivalent martingale measure and the relation between an equivalent martingale measure and numeraire in Black-Scholes' model.