多资产背景下看跌-看涨期权对称性的几何扩展
Geometric extension of put-call symmetry in the multiasset setting
摘要：
在本文中，我们将展示如何将欧式看涨期权和多资产看跌期权与某些称为升降机的凸体联系起来。在此基础上，几何性质可以转化为经济报表，反之亦然。例如，欧洲的买入-卖出平价对应于中心对称性质，而二元市场的概念可以通过相对于平面的反射来解释。众所周知，经典的单变量对数正态模型属于一类具有额外性质的分布，分析上称为看跌期权对称性。这种对称性的几何解释激发了自然的多元扩展。这个扩展的金融含义进行了解释，具有此属性的资产价格分布的特点，并进一步探讨其属性。它还示出了如何将一些多变量的非对称分布对称的幂变换，这是有用的，以调整携带成本。一个特别的注意力是专门的情况下，资产价格驱动的Lévy过程。在此基础上，提出了多资产障碍期权的半静态套期保值方法。
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 Lévy processes. Based on this, semi-static hedging techniques for multiasset barrier options are suggested.
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