摘要翻译：
最新一代的波动性衍生工具超越了方差和波动性互换，探索了我们沿着标的股票价格过程的桥梁对已实现方差和逗留时间进行定价的能力。本文基于Dyson展开和矩方法给出了该问题的算子代数处理，并讨论了其在奇异波动率衍生品中的应用。这些方法是相当灵活的，允许对潜在过程的半参数甚至非参数的规范，包括依赖于状态的局部波动性、跳跃、随机波动性和制度转换。我们发现波动率衍生品特别适合用矩方法来处理，即在几个矩的基础上外推相关路径函数的分布。我们考虑了方差敲除、条件走廊方差互换、gamma互换和方差互换等外来现象，并给出了详细的估值公式。
---
英文标题：
《Moment Methods for Exotic Volatility Derivatives》
---
作者：
Claudio Albanese and Adel Osseiran
---
最新提交年份：
2007
---
分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
--
一级分类：Mathematics        数学
二级分类：General Topology        一般拓扑
分类描述：Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties
连续统理论，点集拓扑，代数结构空间，基础，维数理论，局部和全局性质
--
一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--

---
英文摘要：
  The latest generation of volatility derivatives goes beyond variance and volatility swaps and probes our ability to price realized variance and sojourn times along bridges for the underlying stock price process. In this paper, we give an operator algebraic treatment of this problem based on Dyson expansions and moment methods and discuss applications to exotic volatility derivatives. The methods are quite flexible and allow for a specification of the underlying process which is semi-parametric or even non-parametric, including state-dependent local volatility, jumps, stochastic volatility and regime switching. We find that volatility derivatives are particularly well suited to be treated with moment methods, whereby one extrapolates the distribution of the relevant path functionals on the basis of a few moments. We consider a number of exotics such as variance knockouts, conditional corridor variance swaps, gamma swaps and variance swaptions and give valuation formulas in detail.
---
PDF链接：
https://arxiv.org/pdf/0710.2991