Deep Learning in Asset Pricing

Source: Chen, L., Pelger, M. & Zhu, J. (2024). Management Science 70(2), 714–750.

TL;DR

Estimates the stochastic discount factor (SDF) with deep neural networks, imposing the

no-arbitrage condition that the SDF must price all assets — including conditionally, in every

economic state. The design is adversarial (a GAN-style "discriminator" hunts for the most

mispriced portfolios to form the hardest moment conditions) and uses a recurrent network (LSTM)

to summarize macro state dynamics. The resulting nonlinear SDF delivers strong out-of-sample Sharpe

ratios and ranks characteristic importance.

A general, fully nonlinear SDF that uses both firm characteristics and macroeconomic states, with

asset-pricing theory built into the loss function rather than bolted on.

No-arbitrage moment conditions: the SDF must make pricing errors zero for test-asset returns

interacted with conditioning instruments.

A generative-adversarial setup: one network learns the SDF weights; an adversary chooses the

conditioning portfolios that maximize mispricing, so the SDF is trained against its hardest tests.

An LSTM compresses the macro time series into hidden states used as conditioning variables.

The deep SDF substantially outperforms linear factor models and simpler ML benchmarks

out-of-sample.

Both nonlinearity and macro-state conditioning contribute; a ranking of characteristics by

importance emerges.

A leading example of theory-guided deep learning in finance — embedding no-arbitrage into a neural SDF

— and a capstone of the ML asset-pricing program alongside IPCA, autoencoders, and SDF shrinkage.

GAN/RNN training is delicate and computationally heavy; results require careful regularization.

Interpretability is limited relative to linear/IPCA models.

Chen, L., Pelger, M. & Zhu, J. (2024) — Deep Learning in Asset Pricing — Management Science

Gu, S., Kelly, B. & Xiu, D. (2020) — Empirical Asset Pricing via Machine Learning — Review of Financial Studies

Kozak, S., Nagel, S. & Santosh, S. (2020) — Shrinking the Cross-Section — Journal of Financial Economics