【作者】 陈琪琼；

【导师】 杨向群；

【作者基本信息】 湖南师范大学 ， 概率论与数理统计， 2005， 硕士

【摘要】 期权定价理论是现代金融学的重要组成部分,与投资组合理论、资本资产定价理论、市场有效性理论以及代理问题一起,构成现代金融学的五大理论模块.对于传统的Black-Scholes模型,国内外学者已经做了大量研究工作,获得许多对金融实践有指导意义的结果。但是,在股票价格过程服从对数正态分布的假设下,常数的期望收益率意味着随着时间的变化,股票价格将会有朝同一方向变化的趋势。实证研究表明,股票的预期收益率往往是波动变化的,可能是依赖时间和股票价格的函数,因此众多学者放宽Black-Scholes模型的某些假设条件,提出了各种期权定价模型。 本文考虑的是指数O-U随机过程模型,在该模型下,当股价上升到一定高度后,参数α使股价有下降的趋势,从而更符合股价运动的实际特点。本文运用鞅论、随机分析等数学工具,研究了指数O-U随机过程模型下若干期权定价问题,给出回顾型期权的定价公式,对随机利率下的指数O-U随机过程模型进行定价,并创建带“跳”的指数O-U扩展模型,推导出期权价值方程及相应定价公式。 具体来说,主要得到了如下结果: (1)在股票价格服从指数O-U随机过程,利率为常数的模型假设下,利用风险中性定价原则,分固定履约价和浮动履约价两种情形,得到了回顾型期权的定价公式,并分别给出了买权和卖权的平价关系; (2)在股票价格服从指数O-U随机过程,利率为连续随机利率的模型假设下,给出了期权价值方程以及欧式看涨期权的定价公式; (3)在股票价格服从指数O-U随机过程,利率为跳-扩散过程的模型假设下,给出了期权价值方程以及欧式看涨期权的定价公式; (4)创建带跳跃的指数O-U随机过程扩展模型,并在利率为跳-扩散过程的假设下,给出了相应的期权价值方程以及欧式看涨期权的定价公式。更多还原

【Abstract】 Option pricing theory is an important part of modern finance.Together with the portfolio selection theory,the capital asset pricing theory,the effectiveness theory of market and acting issue,it is regarded as one of the five theory modules in modern finance.Many scholars have done a great deal of researches on Black-Scholes model and obtained a lot of results which is instructive to financial practice.However,supposing that the process of stock price is of lognormal distribution,invariable expectant yields means movement of stock price towards just one direction along with the change of time.Demonstration studies have indicated that the expectant yields of stock prices arc always fluctuant,and may be functions depending on time and stock prices.Therefore,many scholars put forward all kinds of option pricing models by relaxing some assuming conditions of Black-Scholes model.In this dissertation,We consider exponential Ornstein-Uhlenbeck model,which correspond to the actual characteristics of stock price movement better.That is,parameter α cause downtrend of stock price while rising to some degree.This dissertation study option pricing problems under exponential Ornstein-Uhlenbeck model by means of mathematical tools such as martingale theory and stochastic analysis,provide the pricing formula of lookback options,make prices of exponential Ornstein-Uhlenbeck model under the hypothesis of stochastic interest rate,and establish an generalized exponential Ornstein-Uhlenbeck model with "jump" ,to deduce the option value equation and the option pricing formula.In detail we have made main conclusions as follows:(1)Under the hypothesis of exponential O-U model and constant interest rate ,using risk-neutral pricing principle, we obtain the pricing formulas of lookback option in two cases of fixed strike price and floating strike price,and the put-call parity relation is deduced;(2)Under the hypothesis of exponential O-U process model and continuous stochastic interest rate,we obtain the option value equation and the pricing formula of European call option;(3)Under the hypothesis of exponential O-U process model and incontinuous stochastic interest rate,we obtain the option value equation and the pricing formula of European call option;(4)We establish an generalized exponential O-U model with "jump" ,and the option value equation and the pricing formula of European call option are deduced under incontinuous stochastic interest rate model.更多还原