具有违约风险的欧式期权定价模型

发布时间：2018-05-06 15:31

本文选题：分数布朗运动 + 违约风险　；参考：《西安工程大学》2012年硕士论文

【摘要】：期权定价理论是金融工程的核心理论。1973年Black和Scholes在完全资本市场假设基础上提出了著名的Black-Scholes期权定价模型，并给出了其定价公式。然而，许多学者认为分数布朗运动更适合于描述金融市场数学模型，同时，违约风险是金融市场中一个重要因素。本文假设股票价格满足分数布朗运动驱动的随机微分方程，建立分数布朗运动环境下的金融市场数学模型，利用分数布朗运动的随机理论和保险精算方法，研究具有违约风险期权定价问题。全文共分五章。第一章，介绍期权定价理论的历史及研究现状、选题依据以及研究的主要内容。第二章，介绍分数布朗运动的定义及其性质，泊松过程的定义及性质，，同时介绍分数布朗运动随机分析理论及欧式期权的保险精算方法。第三章，假设股票价格满足分数布朗运动驱动的随机微分方程，利用分数布朗运动的随机分析理论及保险精算方法研究了具有违约风险期权定价问题，并得到了它的定价公式。第四章，建立分数跳-扩散过程下的金融市场数学模型，利用分数跳-扩散过程理论及保险精算方法，讨论了具有违约风险期权定价问题，获得了它的定价公式。第五章，总结本文所研究的主要结果，并提出还需进一步研究的问题。
[Abstract]:Option pricing theory is the core theory of financial engineering. In 1973, Black and Scholes put forward the famous Black-Scholes option pricing model on the basis of complete capital market hypothesis, and gave their pricing formulas. However, many scholars think that fractional Brownian motion is more suitable to describe the mathematical model of financial market, and default risk is an important factor in financial market. This paper assumes that the stock price satisfies the stochastic differential equation driven by fractional Brownian motion, and establishes a mathematical model of financial market under fractional Brownian motion environment, using the stochastic theory of fractional Brownian motion and the actuarial method of insurance. This paper studies the pricing of options with default risk. The full text is divided into five chapters. The first chapter introduces the history and research status of option pricing theory. In the second chapter, the definition and properties of fractional Brownian motion, the definition and properties of Poisson process, the stochastic analysis theory of fractional Brownian motion and the insurance actuarial method of European option are introduced. In chapter 3, assuming that the stock price satisfies the stochastic differential equation driven by fractional Brownian motion, we use the stochastic analysis theory of fractional Brownian motion and the actuarial method to study the pricing problem of option with default risk, and obtain its pricing formula. In chapter 4, the financial market mathematical model under fractional hop-diffusion process is established. By using the theory of fractional hop-diffusion process and the actuarial method of insurance, the pricing problem of option with default risk is discussed, and its pricing formula is obtained. Chapter five summarizes the main results of this paper and points out the problems that need further study.
【学位授予单位】：西安工程大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.9;F224

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