波动率期权定价模型的随机叉树方法

发布时间：2018-04-05 09:32

本文选题：波动率期权　切入点：随机波动率模型　出处：《西南财经大学》2013年硕士论文

【摘要】：在目前金融市场中,由金融原生资产回报的波动率变化而带来的风险并不能通过资产组合的方式将其有效地分散开来,即这些原生金融资产的状态和以其为标的物的金融衍生品并不能够有效地规避或对冲嵌套(暗含)在波动率中的所有不确定性。因此为了有效地规避这种风险,投资者就需要增加新的有效对冲资产组合,在此情况下建立在风险源本身即波动率基础上的波动率期权就显示出了其强大的优势,其在套期保值和风险管理方面有重大作用。同时,在最近十几年,含有随机波动率的期权研究已经成为了期权研究领域的热点。当波动率由常数变为随机时,问题的分析难度和解决的复杂程度相比于之前都有一个很大的跳跃。因此,对于随机波动率期权的深入研究对于完善整个期权定价理论是具有深远意义的。本文主要研究了带有随机波动率的四组波动率期权模型的定价问题。在研究此问题上,主要是运用随机叉树(格子算法)来逼近上述的离散模型,设计出有效的算法将整个时间段内的原生资产的运动路径即状态价格计算出来,并推导出各个状态的概率分布,从而完成对上述四组波动率期权模型的定价研究。相比于以前对该类期权定价研究,本文另辟蹊径,将随机叉树方法成功扩展运用到该期权的定价问题上来。通过本文的相关研究,发现无论是在对美式看涨波动率期权还是在对美式看跌波动率期权的定价问题上,随机叉树算法的收敛性、稳定性、有效性都非常好。
[Abstract]:In today's financial markets, the risks associated with changes in the volatility of returns on primary financial assets cannot be effectively dispersed by a portfolio.That is, the state of these primary financial assets and financial derivatives with them as the subject matter can not effectively circumvent or hedge all the uncertainties of nested (implied) volatility.Therefore, in order to avoid the risk effectively, investors need to add a new portfolio of effective hedging assets. In this case, the volatility option based on the risk source itself, that is, volatility, shows its strong advantages.It plays an important role in hedging and risk management.At the same time, in the last ten years, the research of options with random volatility has become a hot spot in the field of options research.When the volatility is changed from constant to random, there is a big jump in the difficulty of analysis and the complexity of solving the problem.Therefore, the in-depth study of stochastic volatility option is of great significance to the improvement of the whole option pricing theory.In this paper, we study the pricing of four groups of volatility options with random volatility.In the study of this problem, the random cross tree (lattice algorithm) is mainly used to approximate the above discrete model, and an effective algorithm is designed to calculate the movement path of the original assets in the whole time period, that is, the state price.The probabilistic distribution of each state is deduced, and the pricing of the above four groups of volatility option models is completed.Compared with the previous studies on the pricing of this kind of options, this paper explores a new approach and extends the stochastic cross tree method successfully to the pricing of this option.Through the relevant research in this paper, it is found that the convergence, stability and effectiveness of the stochastic cross tree algorithm are very good both in the pricing of American call volatility options and American put volatility options.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.91;F224

【共引文献】