A Class Of Options Pricing With Stochastic Lives And An Extension Of The Black-Scholes Formula

In 1973,two great financial theorists and practicers Fisher Black and Myron Scholes published their famous paper "The pricing of Options and Corporate Liability, "which gave the Black-Scholes formula,an explicit formula of the pricing of European Option. This is a breakthrough of modern Mathematical Finance. From then on ,the research of modern Mathematical Finance gained rapid development with tremendous achievements. Most remarkeable of all,the Black-Scholes model has not only been obtained plentify achievements in theory but also is popular when being applied in financial market.The thesis has researched a class of options with stochastic lives systematically on the basis of stochastic lives theory. This paper assumes that a kind of risk, caused by stochastic stopping, is nonsystematic. By means of no arbitrage capital asset pricing and the risk-neutral evalution principle and Feynman-Kac formula, it studies a European call option with stochastic life and the underlying asset obeying diffusing process,included binary option pricing with stochastic life and European power option with stochastic life, and obtains corresponding pricing formula.