英文标题：
《Managing Volatility Risk: An Application of Karhunen-Lo\\`eve
Decomposition and Filtered Historical Simulation》
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作者：
Jinglun Yao, Sabine Laurent, Brice B\\\'enaben
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最新提交年份：
2017
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英文摘要：
Implied volatilities form a well-known structure of smile or surface which accommodates the Bachelier model and observed market prices of interest rate options. For the swaptions that we study, three parameters are taken into account for indexing the implied volatilities and form a \"volatility cube\": strike (or moneyness), time to maturity of the option contract, duration of the underlying swap contract. It should be noted that the implied volatility structure changes across time, which makes it important to study its dynamics in order to well manage the volatility risk. As volatilities are correlated across the cube, it is preferable to decompose the dynamics on orthogonal principal components, which is the idea of Karhunen-Lo\\`eve decomposition that we have adopted in the article. The projections on principal components are investigated by Filtered Historical Simulation in order to predict the Value at Risk (VaR), which is then examined by standard tests and non-arbitrage condition to ensure its appropriateness.
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中文摘要：
隐含波动率形成了一个众所周知的微笑或表面结构，该结构适用于Bachelier模型和观察到的利率期权市场价格。对于我们所研究的掉期期权，在为隐含波动率编制指数时考虑了三个参数，并形成了“波动率立方体”：履约（或货币性）、期权合同到期时间、基础掉期合同期限。应注意的是，隐含波动率结构随时间变化，这使得研究其动态性以更好地管理波动率风险非常重要。由于挥发性在整个立方体中都是相关的，因此最好在正交主成分上分解动力学，这是我们在本文中采用的Karhunen-Lo-eve分解的思想。通过过滤历史模拟对主成分的预测进行研究，以预测风险价值（VaR），然后通过标准测试和无套利条件进行检查，以确保其适当性。
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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
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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