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Deep Learning in a Generalized HJM-type Framework Through Arbitrage-Free Regularization

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  • Anastasis Kratsios
  • Cody B. Hyndman

Abstract

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.

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  • Anastasis Kratsios & Cody B. Hyndman, 2017. "Deep Learning in a Generalized HJM-type Framework Through Arbitrage-Free Regularization," Papers 1710.05114, arXiv.org, revised Dec 2019.
    • Handle: RePEc:arx:papers:1710.05114
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