Risk Preference-based Research For The Pricing Of Some Options In A Fractional Brown Motion Environment

Options is a fnancial derivative product，which frst occurred from USA in themiddle of1970s. About four decades, the study of options theory and its practi-cal application have developed rapidly and reaped rich achievements.Among thesetheory,the pricing of options is one of the core issue about fnancial mathematicsresearch.With the constantly updated and developing of fnancial market,variousnew options(also called exotic options)came into being.In order to satisfy marketdemand,researchers fnd a variety ways to price these new options as objectively aspossible,so the diference between these options theory and true market is more andmore tiny.This paper mainly discusses the pricing of power option、reset option and com-pound option in fnance, using asset pricing and portfolio theroy from stochasticprocess and stochastic analysis. In the condition that the stock price follows Geo-metric Brownian Motion and on the risk preference, we deduce power option、resetoption and four compound option pricing formulas by using option pricing methodssuch as measure transformation and martingale method.In chapter one, we simply introduce the history and research of options.In chapter two, we discuss the pricing of power option at any time before theexpiration and deduce the pricing formulas, underlying the assumptions that thethe stock price follows Geometric Brownian Motion and on the risk preference.In chapter three, we price the reset option which only contain one point of timeunder the condition of risk preference and deduce its value formula at any timebefore the expiration.In chapter four,we discuss the pricing formula of compound option underlyingthe assumptions that stock price follow Geometric Brownian Motion and on riskpreference.In chapter fve, we summarize the main results of this article and gave someproblems that need further efort.