Abstract
A regularization approach to model selection, within a generalized HJM framework, is introduced, which learns the closest arbitrage-free model to a prespecified factor model. This optimization problem is represented as the limit of a one-parameter family of computationally tractable penalized model selection tasks. General theoretical results are derived and then specialized to affine term-structure models where new types of arbitrage-free machine learning models for the forward-rate curve are estimated numerically and compared to classical short-rate and the dynamic Nelson-Siegel factor models.
Highlights
The compatibility of penalized regularization with machine learning approaches allows for the successful treatment of various challenges in learning theory such as variable selection (see Tibshirani (1996)) and dimension reduction (see Zou et al (2006))
The objective of many machine learning models used in mathematical finance is to predict asset prices by learning functions depending on stochastic inputs
There is no guarantee that these stochastic factor models are consistent with no-arbitrage conditions
Summary
The compatibility of penalized regularization with machine learning approaches allows for the successful treatment of various challenges in learning theory such as variable selection (see Tibshirani (1996)) and dimension reduction (see Zou et al (2006)). The objective of many machine learning models used in mathematical finance is to predict asset prices by learning functions depending on stochastic inputs. There is no guarantee that these stochastic factor models are consistent with no-arbitrage conditions. This paper introduces a novel penalized regularization approach to address this modelling difficulty in a manner consistent with financial theory. The incorporation of an arbitrage-penalty term allows various machine learning methods to be directly and coherently integrated into mathematical finance applications. The arbitrage-penalty can be applied to other types of machine learning algorithms with financial applications
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