Pricing Exotic Option In Fractional Brownian

As we all know, with the development of the fnancial industry in the20th century,Financial markets has improved steadily. People often need Avoid the risk and get theinvestment, many fnancial derivatives are designed. Option is both an efective hedginginstruments, but also a wonderful speculative, This makes the option much of the favorof investors and speculators, thought option pricing method,may fnd the pricing theoryof general derivative securities.The option who underlying assets driven by the brownian motion pricing problemshave become more perfect. with long-term memory of the real stock market,which makesthe price movement that use brownian motion to simulate have large deviation, but thefractional brownian motion more better simulate the stock price volatility due to itscharacteristic. Due to the limitations of the theory, the option pricing problem of fractalmarket was the slow progress; In recent years by the development of the theory, optionpricing of fractal market rapid development.In this paper, by using the methods of the fractional risk-neutral valuation princi-ple,fractional Girsanov Theorem,quasi-martingale and measure transformation, we notonly discusses the pricing of Forward Start Options and the Boston Options which theunderlying asset is driven by single fractional Brownian motion, but also discusses thepricing of,collar options and reload option which the underlying asset is driven by multiplefractional brownian motion.The main content of this paper is divided into four chapters:The frst chapter is the introduction section, frstly,we introduce the developmentof options, option pricing and basic pricing problem of option that underlying asset isdriven by multiple fractional brownian motion. Finally,we introduce the main work ofthis article. The second chapter is prior knowledge. In this section, we introduces the conceptionof fractional brownian motion, wick product, quasi-Conditional expectation and quasi-martingale.Finally,we quote some useful lemma.In the third chapter, in the market model which stock is driven by a single fractionalBrownian motion,we focuses on the pricing of the Forward Start Options and BostonOptions which underlying asset is driven by single fractional brownian motion. By themethods of measure transformation and quasi-martingale, we get the general pricing for-mula.In the fourth chapter, in the market model which stock is driven by multiple fractionalbrownian motion,we focuses on the pricing of the Collar Options and Reload Optionswhich underlying asset is driven by multiple fractional brownian motion. By the methodsof measure transformation and quasi-martingale, we get the general pricing formula.