The Research Of The Improved Model Of The Black-scholes Formula

Option pricing theory is always one of the kernel problems on financialmathematics．Together with the portfolio selection theory，the capital asset pricingtheory，the effectiveness theory of market and acting issue，it is regarded as one of thefive theory modules in modem finance．At the beginning of seventy years，FischerBlack and Myron Scholes have made the unprecedented work in the domain of theoption pricing theory，they Proposed the first complete option pricing model，whichnamed the Black—Scholes pricing formula，widely accepted by the theory and theindustrial world with the application，becomes the secondary Great Revolution in afinancial domain．However，in the reality financial market，a mass of finance practice has indicatedthat there is a serious warps between the hypothesis of Black-Scholes model and therealistic markets．This dissertation introduce the option elementary knowledge briefly，the optionpricing theory development history as well as the influence option price factor firstly.Give the definition of the option pricing deviation and had pointed out utilizes severalkind of deviations in the actual market which the Black-Scholes option pricing formulaproduces，finally explained the undulation rate smile theory．From the belief of theprobability of positive returns and traders, I get calls from the historical transaction datareturns probability, and then make decisions from the probability and overcome theBlack-Scholes brought by the European option pricing deviation, find an option andmore consistent with the market price of the option pricing model.Using the simulated data,we give the real diagnosis examination, respectively tocompare the theoretical model and the Black-Scholes model. When the market priceof the call options from investors in the faith, Black-Scholes formula of all three typesof deviation can be verified in the numerical study. To show that the growth rate ofstock returns can replace volatility smile, and will be excluded from the risk neutralanalysis.