Detecting and repairing arbitrage in traded option prices

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.