反射和Lé随机波动率模型的研究

项目名称： 反射和Lé随机波动率模型的研究

项目编号： No.11201111

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 邢小玉

作者单位： 河北工业大学

项目金额： 22万元

中文摘要： 该项目主要研究两种新型随机波动率市场下的期权定价，对冲和参数修正等相关金融问题。这两个研究框架，一个是反射随机波动率模型，另一个是Lé随机波动率模型。前者用反射随机过程描述波动率，和经典的仿射随机波动率模型相似但是又完全独立，后者用随机时间的瞬时变化率代表波动率，是Lé过程和随机时间的复合。特别的，若时间的瞬时变化率用反射随机过程来刻画，即为Lé-反射随机波动率模型。在以上两种新型随机波动率模型的框架下，该项目拟研究普通欧式期权定价。定价问题解决的关键在于对反射随机过程进行某种变换，使其具有类似仿射的解析结构。该项目还研究了Lé随机波动率模型下奇异期权的定价，鉴于模型的复杂性，主要通过对冲策略来实现。该项目的研究进一步丰富发展了随机波动理论，为金融市场提供过了新的研究工具和方法。

中文关键词： 反射过程；斜过程；期权定价；分支过程；参数估计

英文摘要： This project is to study the financial problems, such as option pricing, hedging, parameter calibration and so on, under two new stochastic volatility market models. One of the two research frameworks is the reflected stochastic volatility model, the other is the Lé stochastic volatility model. The former models volatility by using reflected stochastic process, which is somewhat similar to the classic affine stochastic volatility model but in fact wholly independent of it. The latter uses the activity rate of random time to imply volatility, hence is the synthesis of Lé process and random time. In particular, if the activity rate of the time is a reflected process, then the model is Lé-reflected stochastic volatility model. Under the novel stochastic volatility models introduced above, the project considers the European option pricing. The key technique of the pricing problem is that we should apply some transform to the reflected stochastic process, in order to obtain analytical affine structure. Besides, exotic option pricing under Lé stochastic volatility model is another goal of this project. In view of the complexity of this model, this goal will be realized by hedging strategy. The implement of this project further develops and enriches the stochastic volatility theory, and provides financial mark

英文关键词： Reflected process；Skew process；Option pricing；Branching process；Parameter estimation