Autoencoder Market Models for Interest Rates

We propose a highly optimized latent factor representation of the yield curve obtained by training a variational autoencoder (VAE) to curve data from multiple currencies. A curious byproduct of such training is a "world map of latent space" where neighbors have similar curve shapes, and distant lands have disparate curve shapes. The proposed VAE-based mapping offers a high degree of parsimony, in some cases achieving similar accuracy to classical methods with one more state variable.In the second part of the paper, we describe four types of autoencoder market models (AEMM) in Q- and P-measure. Each autoencoder-based model starts from a popular classical model and replaces its state variables with autoencoder latent variables. This replacement leads to a greater similarity between the curves generated by the model and historically observed curves, a desirable feature in both Q- and P-measure. By aggressively eliminating invalid curve shapes from its latent space, VAE prevents them from appearing within the model without intricate constraints on the stochastic process used by the classical models for the same purpose. This makes VAE-based models more robust and simplifies their calibration.Potential applications of the new models and VAE-based latent factor representation they are based on are discussed