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 .
We introduce a regularization approach to arbitrage-free factor-model selection. The considered model selection problem seeks to learn the closest arbitrage-free HJM-type model to any prespecified factor-model. An asymptotic solution to this, a priori computationally intractable, problem is represented as the limit of a 1-parameter family of optimizers to computationally tractable model selection tasks. Each of these simplified model-selection tasks seeks to learn the most similar model, to the prescribed factor-model, subject to a penalty detecting when the reference measure is a local martingale-measure for the entire underlying financial market. A simple expression for the penalty terms is obtained in the bond market withing the affine-term structure setting, and it is used to formulate a deep-learning approach to arbitrage-free affine term-structure modelling. Numerical implementations are also performed to evaluate the performance in the bond market .
R
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
a regularization approach to
R
models. We use this scheme to construct a meta-algorithm which ensures that a wide range of factor estimation schemes return
factor-model selection. The considered model selection problem seeks to learn the closest
R
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
HJM-type model to any prespecified factor-model. An asymptotic solution to this, a priori computationally intractable, problem is represented as the limit of a 1-parameter family of optimizers to computationally tractable model selection tasks. Each of these simplified model-selection tasks seeks to learn the most similar model, to the prescribed factor-model, subject to a penalty detecting when the reference measure is a local martingale-measure for the entire underlying financial market. A simple expression for the penalty terms is obtained in the bond market withing the affine-term structure setting, and it is used to formulate a deep-learning approach to
R
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
affine term-structure modelling. Numerical implementations are also performed to evaluate the performance in the bond market