马尔可夫调制的跳扩散模型下的可转换债券定价

发布时间：2018-04-23 10:19

本文选题：马尔可夫调制 + 可转换债券　；参考：《宁波大学》2014年硕士论文

【摘要】：随着金融市场的不断完善,金融衍生产品层出不穷,其定价问题已成为大量学者和金融工作人员关注的对象.可转换债券作为金融市场中重要的融资衍生产品,如何对其定价也就变的很重要.在实际中,经济市场有时处于稳定状态,而有时又会出现高波动状态.基于此,假定风险资产的价格服从两状态马尔可夫调制的跳扩散模型,当市场处于高波动状态时,风险资产的价格满足跳扩散模型；当市场处于稳定状态时,风险资产的价格满足几何布朗运动模型.我们考虑在该金融模型下可转换债券的定价问题. 论文具体安排如下：第一章首先介绍了可转换债券定价及马尔可夫调制模型的研究现状,接着给出了需要的基本知识,最后介绍了本文的主要工作. 第二章假定标的资产价格服从两状态马尔可夫调制的跳扩散模型,利用无套利和测度变换方法,给出了马尔可夫调制的跳扩散模型下可转换债券的定价公式.另外,利用Monte Carlo模拟方法给出了Black-Scholes模型、跳扩散模型以及马尔可夫调制的跳扩散模型下可转换债券价值的数值解. 第三章在第二章金融模型的基础上,进一步假设市场利率满足Vasicek随机利率模型,其与标的资产价格过程相关,给出了马尔可夫调制的跳扩散模型下可分离交易可转换债券的定价公式.最后,利用Monte Carlo模拟方法给出了可分离交易可转换债券价值的数值解. 第四章考虑带信用风险情况下可转换债券的定价问题.假设可转换债券的违约强度满足均值回归模型,利用鞅方法给出了马尔可夫调制的跳扩散模型下带违约风险的可转换债券定价公式. 第五章最后,我们对论文做了总结以及考虑了今后需要改进的方向.
[Abstract]:With the continuous improvement of the financial market, financial derivatives emerge in endlessly. The pricing of financial derivatives has become the focus of attention of a large number of scholars and financial workers. As an important financial derivative in the financial market, how to price convertible bonds becomes very important. In practice, economic markets are sometimes stable and sometimes highly volatile. Based on this, it is assumed that the price of risk assets is satisfied with the jump diffusion model when the market is in a high volatility state, and when the market is in a stable state, assuming that the price of a risky asset is served by a jump diffusion model modulated by Markov modulation in two states. The price of risky assets satisfies the geometric Brownian motion model. We consider the pricing of convertible bonds under this financial model. The thesis is organized as follows: The first chapter introduces the research status of convertible bond pricing and Markov modulation model, then gives the basic knowledge needed, and finally introduces the main work of this paper. In chapter 2, we assume the jump diffusion model of the underlying asset price from two-state Markov modulation. By using the method of no arbitrage and measure transformation, we give the pricing formula of convertible bonds under the Markovian modulated jump diffusion model. In addition, the numerical solutions of the value of convertible bonds under the Black-Scholes model, the jump diffusion model and the Markov modulated jump diffusion model are given by using the Monte Carlo simulation method. The third chapter is based on the second chapter of the financial model, and further assumes that the market interest rate satisfies the Vasicek stochastic interest rate model, which is related to the underlying asset price process. The pricing formula of separable tradeable convertible bonds in the jump diffusion model of Markov modulation is given. Finally, the numerical solution of the convertible bond value is given by using Monte Carlo simulation method. Chapter 4 considers the pricing of convertible bonds with credit risk. Assuming that the default strength of convertible bonds satisfies the mean regression model, the pricing formula of convertible bonds with default risk is given by using martingale method. In the fifth chapter, we summarize the thesis and consider the direction of improvement in the future.
【学位授予单位】：宁波大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.91

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