交易期权价格中套利的发现与修复
Detecting and repairing arbitrage in traded option prices
摘要：
期权价格数据被用作模型校准、风险中性密度估计和许多其他金融应用的输入。期权价格数据中套利的存在可能导致这些任务的性能不佳甚至失败，因此需要对数据进行预处理以消除套利。相关文献中的大多数注意力都集中在数据的无仲裁平滑和滤波（即去除）上。与通常会改变几乎所有数据的平滑或截断数据的过滤相反，我们建议仅通过必要的和最小的更改来修复数据。我们制定的数据修复作为一个线性规划（LP）的问题，无套利关系的约束，目标是最小化价格的变化，在他们的出价和卖价的界限。通过实证研究，我们表明，所提出的套利修复方法给出稀疏扰动的数据，并快速应用于现实世界中的大规模问题，由于LP制定。此外，我们表明，通过我们的修复方法从价格数据中去除套利可以提高模型校准，增强鲁棒性并减少校准误差。
英文摘要：
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.
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