| This paper is mainly divided into two parts: the further discussion of Black Scholes model and the research of n(n?4) fork tree model for option pricing.In the first part,the model established in this paper is based on the Leland model and the traditional option pricing formula,considering transaction costs at first,and the partial differential equation of European option with transaction cost is obtained,then consider the continuous dividend payment to get the modified option pricing model based on transaction costs,finally,the modified formula of Black-Scholes model is obtained by using the knowledge of discrete model,calculus,probability theory and mathematical statistics,substitution of variables,and some of the conclusions of partial differential equation model.The solution of the modified model is intuitive and easy to understand,and the calculation is simpler.Finally,an example is made to analyze the relationship between the options formula and the traditional option pricing formula with the transaction fee and dividend payment,and the effect of transaction cost and continuous dividend on the option price is clearly illustrated.In the second part,based on the different possibilities of the underlying asset price,combining the advantages of the binary tree method and the trigeminal tree method,the trigeminal tree model is popularized and the four tree model is built on this basis.Because the four fork tree model needs more conditions,the solution process is more complex,therefore,this part combines positive reasoning and reverse reasoning to solve the problem,then,the solution set obtained by the partial relational formula is substituted into the remaining relational formula,it is found that the solution set does not satisfy the remaining relational formulas,it shows that the option pricing of the four forked tree does not exist.Finally,we use the example to further explain the unreasonable pricing of the n fork tree option. |
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