论文标题
在三角洲微笑
Smiles in delta
论文作者
论文摘要
福川（Fukasawa）在[Fukasawa，Math Fancy，2012年]中引入了蝴蝶套利的两个必要条件，要求$ d_1 $和$ d_2 $ d_2 $函数必须降低。在本文中，我们使用Delta中的微笑的参数化表征了满足这些条件的微笑集。我们通过一个实际数字和三个正函数获得集合的参数化。我们还表明，这种微笑及其对称的微笑可以通过两次射击在打击空间中的微笑。我们的结果激发了对表征蝴蝶无款微笑子集的挑战性问题的研究。
Fukasawa introduced in [Fukasawa, Math Financ, 2012] two necessary conditions for no butterfly arbitrage which require that the $d_1$ and $d_2$ functions of the Black-Scholes formula have to be decreasing. In this article we characterize the set of smiles satisfying these conditions, using the parametrization of the smile in delta. We obtain a parametrization of the set via one real number and three positive functions. We also show that such smiles and their symmetric smiles can be transformed into smiles in the strike space by a bijection. Our result motivates the study of the challenging question of characterizing the subset of butterfly arbitrage-free smiles.
