Arbitrage-Free Regularization

We introduce an unsupervised and non-anticipative machine learning algorithm which is able to detect and remove arbitrage from a wide variety models. In this framework, fundamental results and techniques from risk-neutral pricing theory such as NFLVR, market completeness, and changes of measure are given an equivalent formulation and extended to models which are deformable into arbitrage-free models. We use this scheme to construct a meta-algorithm which ensures that a wide range of factor estimation schemes return arbitrage-free estimates and incorporate this additional information into their estimation procedure. We show that using our meta-algorithm we are able to produce more accurate estimates of forward-rate curves, specifically at the long-end. The spread between a model and its arbitrage-free regularization is then used to construct a mis-pricing detection or classification algorithm, which is in turn used to develop a pairs trading strategy. Our theory provides a sound theoretical foundation for a risk-neutral pricing theory capable of handling models which potentially admit arbitrage but which can which can be deformed into arbitrage-free models.