波动率隐藏状态的隐含滤波密度

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

摘要翻译：
利用衍生品价格构造并分析了一个反问题，得到了波动率隐状态下的隐含过滤密度。随机波动率是隐马尔可夫模型(HMM)中的未观测状态，可以通过贝叶斯滤波进行跟踪。然而，衍生数据可以被认为是市场上已经观察到的条件预期，并可以被用作反问题的输入，反问题的解是波动率的隐含条件密度。我们的分析依赖于度量鞅变化的一个规范，我们称之为\textIt{可分性}。该规范有一个乘法成分，表现为市场波动性不确定性的风险溢价。当应用于SPX期权数据时，估计模型和隐含密度产生的方差互换率与VIX波动率指数一致。隐含的密度随着时间的推移相对稳定，并吸收了一些由于期权到期而出现的月度效应，这表明波动性-不确定性溢价可能会因期权到期日而经历周期效应。
---
英文标题：
《Implied Filtering Densities on Volatility's Hidden State》
---
作者：
Carlos Fuertes and Andrew Papanicolaou
---
最新提交年份：
2017
---
分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
--

---
英文摘要：
  We formulate and analyze an inverse problem using derivatives prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using Bayesian filtering. However, derivative data can be considered as conditional expectations that are already observed in the market, and which can be used as input to an inverse problem whose solution is an implied conditional density on volatility. Our analysis relies on a specification of the martingale change of measure, which we refer to as \textit{separability}. This specification has a multiplicative component that behaves like a risk premium on volatility uncertainty in the market. When applied to SPX options data, the estimated model and implied densities produce variance-swap rates that are consistent with the VIX volatility index. The implied densities are relatively stable over time and pick up some of the monthly effects that occur due to the options' expiration, indicating that the volatility-uncertainty premium could experience cyclic effects due to the maturity date of the options.
---
PDF链接：
https://arxiv.org/pdf/1203.6631

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏0 回帖

关键词：波动率 Quantitative Expectations uncertainty conditional 密度 filtering conditional 规范 state