Research For The Pricing Of Power Option And Its Variation Options

Option is one of the most important and basic financial derivative tools. Financial derivative tool is a new type financial tool that its price ultimately depends on another asset (Underlying asset).In another word, the price of options is derivatived by the price of its underlying asset.Now,options pricing is one of the core issues for the financial mathematics study.Fisher Black & Myron Scholes's seminal paper "The Pricing of options and corporate liabili-ties" published in 1973 marks the beginning of the financial derivative Securities pricing theory.This article calculated the pricing formula and showed the proof of the power option under different conditions,and then researched the pricing of its variation options.The first chapter introduces the preliminary knowledge of the options and option pricing theory, and describes the B-S option pricing model, this chapter provides the theoretical basis for this article.The second chapter at first studys the general European power option pricing model ,and then studys two kinds of its variation options that called Up-and-Out power option and Lookback power option. This chapter detailly derived the pricing formula with the martingale and the Risk-Neutral Measure, and these methods and techniques also apply to the calculation of other option pricing formula.The main content of the third chapter is the power option pricing under the Frac-tional Brownian Motion.In the forth chapter, we obtained the pricing formular of power reload option under the constant rate and the vasicek rate.The final chapter summarizes the paper, points out the significance of this study and the areas for improvement,and at last proposed the further research.