基于随机利率模型的欧式期权定价研究

发布时间：2018-03-25 09:02

本文选题：期权定价　切入点：随机利率　出处：《哈尔滨工程大学》2012年硕士论文

【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.
[Abstract]:This paper mainly discusses the European option pricing problem based on stochastic interest rate model, including the following aspects: stochastic analysis and the basic theory of option pricing, Based on the generation and background knowledge of Black-Scholes equation for derivative securities without dividend payment, the Black-Scholes formula is solved by using partial differential method and equivalent martingale measure method, respectively. This paper discusses the pricing of European options under the specific stochastic interest rate model and the general stochastic interest rate model, and under more complicated assumptions, deduces the pricing formula of the hopped European option with dividend under the stochastic interest rate model. In this paper, the discussion of option pricing is explained by taking stock as the underlying asset, and the behavior mode of stock price is explained in detail, and the combination of derivative securities and underlying stock is constructed under the framework of no arbitrage. By using the partial differential method and the equivalent martingale measure method, the Black-Scholes equation corresponding to the price of derivative securities is derived, and the intrinsic relations of the two methods are given. The emphasis of this paper is to improve the inherent assumptions of the Black-Scholes model. Under the general stochastic interest rate model, whether the interest rate is related to the source of stock volatility, In the end, the analytical solution of European option pricing with jump based on stochastic interest rate model is given, which further extends the Black-Scholes option pricing model.
【学位授予单位】：哈尔滨工程大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9

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