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摘要翻译：
本文给出了在利维市场上欧式期权和异国情调期权的套期保值策略。应用泰勒定理，在不同的市场假设下，如存在幂跳资产或矩互换，构造了动态套期保值投资组合。在欧式期权或一揽子欧式期权的情况下，实施静态对冲。结果表明，可以实现完美的套期保值。Delta和gamma对冲策略通过投资于依赖于同一基础资产的其他交易衍生品而扩展到更高时刻对冲。这一发展具有实际重要性，因为其他衍生工具可能很容易获得。瞬间掉期或权力跳跃资产通常不进行清算交易。本文给出了最小方差投资组合如何被用来对冲定价函数泰勒展开式中的高阶项，只投资于无风险银行账户、基础资产和潜在的方差互换。给出了套期保值策略的数值算法和性能，表明了推导结果的实用价值。
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英文标题：
《Hedging strategies and minimal variance portfolios for European and
exotic options in a Levy market》
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作者：
Wing Yan Yip, Sofia Olhede, David Stephens
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最新提交年份：
2008
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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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
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英文摘要：
This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European options, static hedging is implemented. It is shown that perfect hedging can be achieved. Delta and gamma hedging strategies are extended to higher moment hedging by investing in other traded derivatives depending on the same underlying asset. This development is of practical importance as such other derivatives might be readily available. Moment swaps or power jump assets are not typically liquidly traded. It is shown how minimal variance portfolios can be used to hedge the higher order terms in a Taylor expansion of the pricing function, investing only in a risk-free bank account, the underlying asset and potentially variance swaps. The numerical algorithms and performance of the hedging strategies are presented, showing the practical utility of the derived results.
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PDF链接：
https://arxiv.org/pdf/0801.4941
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