论文标题
期权价格的$ C^2 $ $ c^2 $的无套利插值
An arbitrage-free interpolation of class $C^2$ for option prices
论文作者
论文摘要
本文介绍了Carr和Nadtochiy的局部方差伽马模型的简单公式，并具有分段线性的局部方差函数。新的公式允许将模型有效地校准到市场期权报价。在一小部分引号上，在一毫秒内实现了精确的校准。这有效地导致了$ c^2 $类的无套利插值。当引号嘈杂时，本文提出了一个良好的正则化。最后，它证明了一个模型AT-The Money的问题，该模型也存在于Andreasen和Ange的相关一步有限差异技术中，并为其提供了两种解决方案。
This paper presents simple formulae for the local variance gamma model of Carr and Nadtochiy, extended with a piecewise-linear local variance function. The new formulae allow to calibrate the model efficiently to market option quotes. On a small set of quotes, exact calibration is achieved under one millisecond. This effectively results in an arbitrage-free interpolation of class $C^2$. The paper proposes a good regularization when the quotes are noisy. Finally, it puts in evidence an issue of the model at-the-money, which is also present in the related one-step finite difference technique of Andreasen and Huge, and gives two solutions for it.
