Based on the fractals of the capital market , this paper derives a fractional geometric brownian motion model for the stock price . this paper constructs a formula for option pricing on the basis of the fractional brownian motion model . on the one hand , this paper draws on the latest researches in this field : the explicit formula for european option pricing ? the fractional brownian motion formula for option pricing ; on the other hand , the analytical solution is derived through the monte carlo simulation 基于资本市场的分形特性,本文接着推导出股票价格变化的几何分数布朗运动模型;随后,在该模型的基础上,本文研究了在分数布朗运动环境下的期权定价模型,一方面引用了国际上最新的研究成果:在分数black - scholes完全市场下,欧式期权定价的显式公式-分数black - scholes期权定价公式;另一方面,又运用蒙特卡罗模拟法,通过模拟股票价格变化的路径并进行贴现,得出了欧式期权价格的数值解。
Using equivalence martingale probability measure given permission to be installed once and twice with the european style options pricing formula , and focus on exploring the options pricing technically allowed to be loaded with a european - style options for the manager incentive options with the standard incentive comparative analysis 利用等价鞅概率测度给出允许再装一次和两次的欧式再装期权的定价公式,并着重从期权定价技术上探讨允许再装一次的欧式再装期权用于经理激励与标准期权的激励比较分析。
Evading risk in financial trading market cries for pricing options to a nicety . asian option , as the most flourish options in the finace market , the pricing has been focused on always . the exact pricing formula for the geometric average asian option had existed , but as to the european - style arithmetic average asian option , due to the dependence structure between the prices of the underlying asset , no analytical formula exists . on the hypothesis that the market is frictionless and without transaction costs 、 on the base of b - s ’ s and in the binomial tree model , we provide several algorithms for computing an accurate value of the european - style arithmetic average asian option . following rogers and shi and by jensen ’ s inequality , many different upper and lower bounds are provided ; meanwhile a formula have got by the comonotonicity and approximating the distribution function . all of the algorithms are easy for programming . with the development of computer , more accurater price can be computed quickly . and numerical example proved that these algorithms are very accurate 对于几何平均亚式期权它的定价相对简单,已经给出了定价公式。对于算术平均亚式期权,它的未定权益具有轨道依赖特性,一直没有得到它的定价方程的解析解形式。本文基于对市场是无摩擦且在没有交易费用的情况下,在b - s模型下,利用二叉树模型给出了算术平均亚式期权定价方法;并总结了利用jensen ’ s不等式给出的各种不同情况下的上下界;同时应用共单调性和近似分布函数的方法也给出了算术平均亚式期权价格的近似公式。
And the unbelievable increase happened in the filed of derivatives , the issued financial derivatives in 1996 is totally around 3 . 5 trillion u . s . dollars , and among these transactions , about 2 . 5 trillion u . s . dollars was otc , and the rest was happened in the official exchange Vasicek根据vasicek随机模型推导出零息债券的平均价格,奥托在其1998年的论文中用统计物理学中的路径积分方法重新推导了基于vasicek随机模型的零息债券平均价格的定价公式,并得到了相同的结论。
Q ( t ) ) dt + ( t ) dwtq ] , and the interest rate of the riskless asset 、 the volatility rate and the dividend rate of stock are non - random functions of time , the pricing formula of two - points reset option is obtained by using martingale and stochastic analysis knowledge 。 following the thought of merton , chapter five depicts the asset price motion with ito Q ( t ) ) dt + ( t ) dwtq ] ,且无风险利率、股息率以及波动率为时间的非随机函数,并借助鞅和随机分析知识给出了两点重设型期权的定价公式。第五章按照merton的思想,用以下ito
Study work mainly is : part one , look back and look ahead the financial development history and present situation that derives market and the futuristic tendency , summarize domestic and international theory and method about venture capital investment , discuss establishment and develop the financial necessariness and important meaning of our country that derives market ; part two , establishthe relation between investment risk and the radom expectation effectiveness of investor ? verage stochastic dominance of asset profit ; part three , covari - ance matrix in mean - variance model is analysed with sensitivity analysis and fuzzy analysis ; part four , have looked back the concept of option , the price relation of option and black - scholes option price formula , have put forward option price formula of the discounted value of option present value ; part five , have looked back the financial concept and its classfication that financial derivatives risk , have summarized financial risk management theory , measured and assessed methods of financial derivatives risk 主要研究工作为：第一章，回顾和展望金融衍生市场的发展历史、现状和未来，综述国内外关于风险投资的理论与方法，论述建立和发展我国金融衍生市场的必要性及重要意义；第二章，建立投资者的随机期望效用与投资风险之间的关系? ?平均随机占优；第三章，均值方差模型协方差矩阵的灵敏度分析与模糊分析；第四章，回顾了期权的概念、期权的价格关系和black - scholes期权定价公式，提出了欧式看涨期权价格的折现值所满足的微分方程；第五章，回顾了金融衍生品风险的概念及其分类，总结了金融衍生品的风险管理理论和金融衍生品风险计量和评估方法。
The results show that : ( l ) adoption of the intermittent mean price instead of the point price at the end of the option will help to reduce the chances of profit - making manipulated by managers and to curb the manager ' s motive to control the stock price ; ( 2 ) generally speaking , stock price of mean price option is more incentive to the managers than that of the black - scholes ; ( 3 ) when the stock market slumps at the end of the option , mean price option will ensure a moderate insurance for the managers ; ( 4 ) when stock price slumps alone with the overall situation of the stock market in the intermittent option , mean price option . however , will be inefficient as an incentive . chapter four addresses the questions concerning the manager ' s manipulation of the stock price , and the increase of the option risks because of long - term slump of the stock market 第三部分包括第三至五章，第三章针对时点价格容易被控制和时点价格的波动性太大，增加了经理期权的风险等问题，研究采用期权期内的平均价格替代期权期末的时点价格计算经理股票期权收益，构建了几何型平均价格期权定价公式，并与black ? scholes期权定价公式进行了定量对比分析，结果表明： ( 1 )采用期权期内平均价格替代期权期末时点价格有利于降低经理通过操纵股价的牟利机会，遏制经理操纵股价的动机； ( 2 )一般条件下，平均价格期权股票价格对经理的激励作用优于标准期权； ( 3 )当临近期权期末股价下跌时，平均价格期权能为经理提供适度保险； ( 4 )当期权期内，股票受大市持续走弱影响而下跌时，平均价格期权失去了激励作用。
Chapter two analyses the problems that fixes the convertible bond price in our country . many listed companies generally use european option price at the formula , namely black - scholes model . because of the multiple option nature and the american option nature contained in the transferable bond , black - scholes model ca n ' t be applied mechanically to fix the price of the convertible bond 第二章分析了可转换债券定价在我国所存在的问题，即从我国上市公司发行可转换债券的公告来看，一般都使用欧洲期权定价公式，这是由1973年fischerblack和myronscholes在其《期权和公司负债定价》的著名论文中所建立起的欧式期权定价解析表达式，即black - scholes模型而成。
Supposing the company ' s value satisfies a certain probability distribution , then , we can calculate the company ' s value in the future as well as its connotative undulation basing on the relationship and a certain option pricing formula , which is based on the supposing talked above . further , we can calculate the company ' s expected default frequency . by now , the goal to measuring the company ' s credit risk has realized 如果假设公司价值波动服从某一概率分布，那么根据与此概率分布相对应的期权定价公式，以及股票价格波动率与公司资产价值波动率之间的函数关系，即可求出公司未来某个时点的期望价值及其隐含波动率，并进一步计算出此时点公司违约的概率，由此便实现了对公司信用评级的目的。
And then , the thesis import a thrice - polynomial technology to depict the yield curve of shanghai stork exchange market and gained the yield curve chart . under one factor model hypothesis , deduce the bond pricing formulae . based on 1945 data of buy - back rate in banking market , the thesis use ols and gmm estimation technologies to estimate the parameters of vasicek model , cir model , and ckls model , and verify which model can explain the china market ’ s short rate ’ s wave 然后,从实证的角度,用三次多项式来拟合上交所国债收益率曲线,并得出收益率曲线图,在单因素模型推导了动态理论期限结构下的债券定价公式,并以1945个中国银行间债券市场7天回购利率数据作为短期利率的代表,验证vasicek模型、 cir模型与ckls模型是否适用中国短期利率的波动行为,估计出三个模型的参数。
