基于局部风险最小化的GARCH期权

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：
我们将Foellmer，Schweizer和Sondermann提出的二次套期保值方案应用于欧洲未定产品，其基础资产是用GARCH过程建模的，并证明了关于物理度量的局部风险最小化策略是存在的，即使相关的最小鞅度量只有在有界创新存在的情况下才可用。更重要的是，由于这些局部风险最小化策略通常是复杂且难以评估的，我们引入了Girsanov类风险中性测度，得到了更易于处理和有用的结果。针对这一问题，我们重点研究了具有高斯新息的GARCH时间序列模型，给出了与峰度有限性有关的充分条件，在此条件下，鞅测度在二次套期保值条件下是合适的。当这个等价鞅测度适用于价格表示时，我们可以从它中恢复出Duan和Heston-Nandi的经典定价公式，以及改进文献中提出的套期保值方案的性能。
---
英文标题：
《GARCH options via local risk minimization》
---
作者：
Juan-Pablo Ortega
---
最新提交年份：
2010
---
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
--
一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
--

---
英文摘要：
  We apply a quadratic hedging scheme developed by Foellmer, Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process and show that local risk-minimizing strategies with respect to the physical measure do exist, even though an associated minimal martingale measure is only available in the presence of bounded innovations. More importantly, since those local risk-minimizing strategies are in general convoluted and difficult to evaluate, we introduce Girsanov-like risk-neutral measures for the log-prices that yield more tractable and useful results. Regarding this subject, we focus on GARCH time series models with Gaussian innovations and we provide specific sufficient conditions that have to do with the finiteness of the kurtosis, under which those martingale measures are appropriate in the context of quadratic hedging. When this equivalent martingale measure is adapted to the price representation we are able to recover out of it the classical pricing formulas of Duan and Heston-Nandi, as well as hedging schemes that improve the performance of those proposed in the literature.
---
PDF链接：
https://arxiv.org/pdf/0904.1078

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：GARCH ARCH RCH ARC Quantitative 序列 measure Foellmer 局部 新息