Several Models, European Option Pricing

In mathematical finance,the pricing of the rights and interests plays an important role,Since the Black and Scholes(Black and scholes) published an pioneering papers on the options pricing in 1973,a large number of options on the valuation was flourishing.Merton,Cox,Arthur Ruhinstein,and some other scholars have been carried out important promotional and widely used on this theory,the option pricing theory and the use have been developed and enriched constantly, and it has been extended to more abstract theories and interests of undetermined significance of a broader asset pricing theory.The latest research of modem financial theory is the introduction of Martingale,under the assumption that the financial markets is effective,the price of security equivalent to a Martingale random process.The Martingale method initiated by Karatzas and Shreve and others directly introduced the martingale theory into modem financial theory,the using of the concept of the equivalent martingale measure on derivative securities pricing,the results can not only profoundly reveals the laws of financial markets,but also can provide an effective method.This paper on the basis of a large number of scholars,the past 30 years to claim the pricing and development of the theory and evolution for clues,Use martingale theory,stochastic analysis, and other modem mathematical tools,mainly to study options pricing,on the basis of the to relaxes of market conditions,obtain the corresponding pricing model.This study as follows:Chapter 1,the Introduction,reviews the development,the study status and the meaning of option pricing theory.The second chapter introduces a new measure—the dual martingale measure,The pricing question of the uncertain rights is to ask the expectation under the equivalent measure of the discount of their income interests functions,usually uses the partial non-risk bank account for the discount Charge unit is,but antithesis martingale measure use the risky assets denominated in units for the discount measure.This chapter use martingale measure and the dual martingale measure on a dividend payment options pricing to obtain the Martingale and dual Martingale models.And compared the two models,obtains their relationship. ChapterⅢ,the majority researches on the formula BS basises on the stock prices subject to Brownian motion,and on the conditions that the price is determined,Uncertainty it does not apply to the stochastic executive price to price the derivative securities,This chapter studies the option pricing on the random executive price,obeys Option Pricing Model that the shares subject to the O-U(Ornstein-Uhlenback) process and the random executive price.ChapterⅣ,insurance actuarial method,Through the comparison of insurance actuarial method with the arbitrage fixed price,has manifested the superiority of this method,then deduces the models that the stock prices are subject to O-U process and the Jump-diffusion process.