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摘要翻译：
在本文中，我们展示了如何将多个资产的欧式看涨和看跌期权与某些称为lift Zonoid的凸体联系起来。基于此，几何性质可以转化为经济报表，反之亦然。例如，欧洲的看涨-看跌平价对应于中心对称性，而对偶市场的概念可以用相对于平面的反射来解释。经典的单变量对数正态模型属于一大类分布，具有一个额外的性质，解析上称为put-call对称性。这种对称性的几何解释激发了自然的多元扩展。解释了这种扩展的金融含义，刻画了具有这种性质的资产价格分布，并探讨了它们的进一步性质。文中还说明了如何通过功率变换将一些多元非对称分布与对称分布联系起来，这种功率变换有助于调整携带成本。特别关注由L\'evy过程驱动的资产价格的情况。在此基础上，提出了多资产障碍期权的半静态套期保值技术。
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英文标题：
《Geometric extension of put-call symmetry in the multiasset setting》
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作者：
Ilya Molchanov and Michael Schmutz
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最新提交年份：
2009
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分类信息：
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
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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：
In this paper we show how to relate European call and put options on multiple assets to certain convex bodies called lift zonoids. Based on this, geometric properties can be translated into economic statements and vice versa. For instance, the European call-put parity corresponds to the central symmetry property, while the concept of dual markets can be explained by reflection with respect to a plane. It is known that the classical univariate log-normal model belongs to a large class of distributions with an extra property, analytically known as put-call symmetry. The geometric interpretation of this symmetry property motivates a natural multivariate extension. The financial meaning of this extension is explained, the asset price distributions that have this property are characterised and their further properties explored. It is also shown how to relate some multivariate asymmetric distributions to symmetric ones by a power transformation that is useful to adjust for carrying costs. A particular attention is devoted to the case of asset prices driven by L\'evy processes. Based on this, semi-static hedging techniques for multiasset barrier options are suggested.
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PDF链接：
https://arxiv.org/pdf/0806.4506
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