带跳的随机波动率下离散情形的方差互换定价研究

发布时间：2018-01-03 01:03

本文关键词：带跳的随机波动率下离散情形的方差互换定价研究　出处：《西南财经大学》2014年硕士论文　论文类型：学位论文

【摘要】：方差互换作为一种单纯对冲波动率风险暴露的工具,在风险管理方面发挥着重要的作用。美国《风险》杂志的数据显示,在过去的几年中,方差互换的交易量几乎每年翻一番。近年来,东南亚经济危机、自2007年以来的次贷危机等使得全球经济出现难以预见的暴涨和暴跌现象,于是,在方差互换定价的模型中引入刻画这种现象的跳扩散以及随机波动率变得越来越有必要；同时鉴于实际生活中方差互换的现金流交换并不是连续进行的,因此,离散情形下的方差互换定价研究也将越来越受到重视。本文是在Song-Ping Zhu和Guang-Hua Lian的研究基础上进行的。不同的‘是,为使模型更加符合实际,我们在标的资产价格的演化过程中加入了连续红利率和跳扩散模型。作为本文的主要贡献,首先,我们证明了刻画跳扩散的复合泊松过程和一般布朗运动的独立性,这样便可以将实现方差分解成分别由跳扩散和布朗运动驱动的两个部分独立研究；进一步的,在跳扩散模型方面,我们引入了用正态分布刻画跳幅度的Merton模型和用双指数分布刻画跳幅度的S.G.Kou模型,并分别给出了这两种情形下离散形式的方差互换的解析解；最后,我们证明离散情形下得到的方差互换的解析解在样本频数无限大的情况下将渐进收敛于其连续形式的解析解,并研究了跳扩散的各个参数对方差互换的影响。
[Abstract]:Variance swaps, as a simple tool for hedging volatility exposure, play an important role in risk management. The volume of variance swaps almost doubled every year. In recent years, the economic crisis in Southeast Asia and the subprime mortgage crisis since 2007 have made the global economy rise and plummet unpredictably, so. It is more and more necessary to introduce the jump diffusion and random volatility to describe this phenomenon in the variance swap pricing model. In view of the fact that the cash flow exchange of variance swap is not continuous in real life, therefore, the study of variance swap pricing in discrete case will be paid more and more attention. This paper is based on the research of Song-Ping Zhu and Guang-Hua Lian. We add the continuous red interest rate and jump diffusion model in the evolution of underlying asset price. As the main contribution of this paper, first of all. We prove the independence of the composite Poisson process and the general Brownian motion, which can decompose the realization variance into two parts, which are driven by the jump diffusion and the Brownian motion, respectively. Furthermore, in terms of jump diffusion model, we introduce the Merton model to describe the jump amplitude by normal distribution and the S.G. Kou model to describe the jump amplitude by double exponential distribution. The analytical solutions of the discrete form of variance exchange in these two cases are given respectively. Finally, we prove that the analytic solution of variance exchange obtained in discrete case will converge asymptotically to its continuous form when the sample frequency is infinite. The effects of the parameters of jump diffusion on the interchangeability of each parameter are studied.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：O211.6;F830.91

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