论文标题
检测和维修交易期权价格的套利
Detecting and repairing arbitrage in traded option prices
论文作者
论文摘要
期权价格数据用作模型校准，风险中性密度估算和许多其他财务应用的输入。期权价格数据中套利的存在可能导致这些任务的性能差甚至不佳，从而预先处理数据以消除必要的套利。相关文献中的大多数注意力都致力于无套利的平滑和过滤（即删除）数据。与平滑相反，平滑性通常会更改几乎所有数据或过滤（截断数据），我们建议仅通过必要和最小的更改来修复数据。我们将数据维修提出为线性编程（LP）问题，在该问题中，无肢关系是约束，目的是最大程度地减少价格的变化并提出价格范围。通过实证研究，我们表明，提出的套利修复方法给出了数据稀疏的扰动，并且由于LP配方而应用于现实世界中的大规模问题时，它很快。此外，我们表明，通过我们的维修方法从价格数据中删除套利可以通过增强的鲁棒性和减少校准误差来改善模型校准。
Option price data are used as inputs for model calibration, risk-neutral density estimation and many other financial applications. The presence of arbitrage in option price data can lead to poor performance or even failure of these tasks, making pre-processing of the data to eliminate arbitrage necessary. Most attention in the relevant literature has been devoted to arbitrage-free smoothing and filtering (i.e. removing) of data. In contrast to smoothing, which typically changes nearly all data, or filtering, which truncates data, we propose to repair data by only necessary and minimal changes. We formulate the data repair as a linear programming (LP) problem, where the no-arbitrage relations are constraints, and the objective is to minimise prices' changes within their bid and ask price bounds. Through empirical studies, we show that the proposed arbitrage repair method gives sparse perturbations on data, and is fast when applied to real world large-scale problems due to the LP formulation. In addition, we show that removing arbitrage from prices data by our repair method can improve model calibration with enhanced robustness and reduced calibration error.
