Machine Learning for Interest Rates: Using Auto-Encoders for the Risk-Neutral Modeling of Yield Curves

Abstract

In this paper, we use autoencoders (AE) to capture the historical dependence structure of interest rates, and introduce risk-neutral forward rate dynamics that are consistent with a given AE curve manifold. We first derive a general condition for the AE-based forward-rate curve to admit a no-arbitrage evolution. Then, by allowing a small convexity-driven deviation from the AE curve manifold, we derive a risk-neutral modeling framework that is arbitrage-free and incorporates the information built into the AE (low-dimensional) curve manifold. Finally, we showcase numerical results based on historical market swap data for multiple currencies, visualizing graphically some of our key concepts.

This paper is an improved version of "Autoencoder-Based Risk-Neutral Model for Interest Rates", which can be downloaded at: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4836728 Besides improving the notation, the flow of exposition, and fixing some typos, we here introduce critical new results in the form of an explicit and constructive methodology for creating risk-neutral models consistent with historical rate observations and their joint evolution.