基于二叉树型的期权定价.docx

目录摘要1ABSTRACT2第一章绪论31.1背景介绍31.2 本文的主题3第二章预备知识42.1 期权42.2二叉树方法42.2.1 方法概述42.2.2二叉树方法的优点和缺点62.2.3 风险中性定价62.3 Black-Scholes 期权定价模型72.3.1模型来源72.3.2风险中性定价72.3.3模型假设82.3.4Black-Scholes期权定价公式8第三章本论93.1期权定价的二叉树模型93.1.1参数确定93.1.2资产价格树形113.1.3通过树形倒推113.1.4代数表达式123.2 例子模拟计算和结果分析123.3 模型改进——三叉树15第四章结论16谢辞及参考文献17谢辞17参考文献18附录20计算过程中涉及算法20摘要Black-Scholes 期权定价模型为期权定价尤其是欧式期权定价提供了良好的解析结果，而Black-Scholes 公式是此模型的核心，但是此公式并不能很好地求解出在很多衍生模型例如亚式期权以及美式期权中的解析解。二叉树方法作为一种数值方法，同时也是图论中一种重要方法，应用于期权定价问题中，它有了更特别的演变。本文利用二叉树方法计算期权定价的数值解，用二叉树方法迭代多次，求出较为准确的期权价格。通过B-S公式得出的结果与二叉树方法得到的结论对比，分析二叉树方法模拟的优点和缺点。同时，我们还要研究二叉树模拟的步数与预测结果和精度间的关系，从而更加深入了解二叉树方法。然而，我们在模型中设立了许多条件，这些都使模型离真实情况越来越远，我们必须不断发展模型，完善模型。三叉树方法正是二叉树方法的合适补充。关键词：二叉树方法，Black-Scholes 模型，风险中性定价ABSTRACTBlack-ScholesFormulaisthecoreofBlack-ScholesOptionPricingModelwhichprovidesapracticalmethodforoptionpricing.Ithasanalyticalsolutionswithgoodpropertiesinsomespecialsituations,forinstance,Europeanoptions.However,theanalyticalsolutionisdifficulttofindinmanyderivativemodelslikeAsianoptions and American option.Asasortoftypicalstatisticalsimulationmethod,Binomial treeplaysveryimportantrolesinGraph Theory and othersignificantacademicfields.When it applies to the option price,binomial tree method has much more special use.Themainideaisthat we put the binomial tree into effect,reapply this method and get numericalresultsofoption price.By comparing the results of Black-Scholes formula with the results of binomial tree method,we come to the advantages and disadvantages of both method. Meanwhile,the study of the steps of binomial tree method is also included to get its relationship with the method’s results and accuracy,which leads us to understand this method deeply and rightly.However,we set many extra conditions,which pushes the situation further away from the real situation.The simple binomial tree method is supposed to be improved constantly in case the finance market changes ceaselessly. Ternary tree is a good supplement for the binomial tree.Keywords:Bino