【作者】 肖斌；

【导师】 郑晓阳；

【作者基本信息】 哈尔滨工程大学 ， 应用数学， 2012， 硕士

【摘要】 本文主要讨论基于随机利率模型的欧式期权定价问题，包括以下几个方面的内容：随机分析和期权定价基本理论，基于无红利支付股票的衍生证券所必须满足的Black-Scholes方程的产生及其背景知识，利用偏微分方法和等价鞅测度法分别求解Black-Scholes公式，在特定随机利率模型和一般随机利率模型下对欧式期权定价进行讨论，以及在更加复杂的假设下，推导随机利率模型下支付红利的带跳的欧式期权的定价公式.本文对期权定价的讨论都是以股票作为标的资产来说明，对股票价格的行为模式进行了详细的阐述，并且在无套利框架下，通过构造包含衍生证券和标的股票的组合，利用偏微分方法和等价鞅测度法分别推导出符合衍生证券价格的Black-Scholes方程，总结性地给出了两种方法的内在联系．本文着重点在于改进Black-Scholes模型的固有假设条件，在一般随机利率模型下，就利率与股票波动源是否相关两种情况，对原有的期权定价公式进行延拓.本文最后还给出了基于随机利率模型支付红利的带跳的欧式期权定价的解析解，从而进一步拓展了Black-Scholes期权定价模型.更多还原

【Abstract】 This thesis mainly discusses the problem of European option pricing based on thestochastic interest rate model, including the following aspects: stochastic analysis and optiontheory, the generation and background knowledge of Black-Scholes formula wherein theformula is satisfied by the price of any derivative security based on stock without dividend,the solution of Black-Scholes formula under the partial differential equation method and theequivalent martingale measure method, the discussion for European option pricing based onparticular stochastic interest rate model and the general stochastic interest rate model, as wellas in the more complex assumption, the derivation of European option pricing with thestochastic interest rate,paid dividend and jump-diffusion.The discussion of this thesis is based on the option pricing which takes stock asunderlying asset, and it focuses on the behavioral pattern of stocks. The Black-Scholesdifferential equation satisfying all derivative securities’ prices is deduced by forming asecurity group including a derivative security and a certain underlying stock meanwhileapplying the partial differential equation method and the equivalent martingale measuremethod and the relationship between the two method is given summarily. This thesis focuseson the improvement of inherent assumptions of the Black-Scholes model. It develops theoriginal option pricing formula based on the stochastic interest rate model whether the interestrate and stock is related or not. A closed form solution of European option pricing with thestochastic interest rate, paid dividend and jump-diffusion is given at the end of the thesis andit indeed expands the Black-Scholes model.更多还原