The Pricing Of Derivative Ecurities Under Fractal Market

In 1973, two great financial theorists and practices 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 remarkable of all, the Black-Scholes model has not been obtained plentiful results in theoretical research, but also been applied in financial market broadly. In 1990s the annual transaction volume in global derivative securities market achieved 50,000 billion dollars.In this dissertation, on the basis of the stochastic integral of the fractional Brownian motion, we studied the pricing of derivative securities.First we introduce the history of mathematical finance, especially its main research content and results.Then we introduce the definition, properties and quasi-conditional expectation and quasi-martingale of the fractional Brownian motion.On the basis we discuss the pricing of European warrant under fractal market. About European warrant without and with dividends payments, we give their pricing formulas. We then give the pricing formulas of European warrant and Spread Option under Multi-noise.At last, we discuss the pricing of European foreign currency Option under fractal market. About foreign currency contingent claims and European foreign currency, we give their pricing formulas. We then give the pricing formulas of European foreign currency Option under Multi-noise.