Deep Learning in Asset Pricing

Abstract

We propose a novel approach to estimate asset pricing models for individual stock returns that takes advantage of the vast amount of conditioning information, while keeping a fully flexible form and accounting for time-variation. Our general non-linear asset pricing model is estimated with deep neural networks applied to all U.S. equity data combined with a substantial set of macroeconomic and firm-specific information. We estimate the stochastic discount factor that explains all asset returns from the conditional moment constraints implied by no-arbitrage. Our asset pricing model outperforms out-of-sample all other benchmark approaches in terms of Sharpe ratio, explained variation and pricing errors. We trace its superior performance to including the no-arbitrage constraint in the estimation and to accounting for macroeconomic conditions and non-linear interactions between firm-specific characteristics. Our generative adversarial network enforces no-arbitrage by identifying the portfolio strategies with the most pricing information. Our recurrent Long-Short-Term-Memory network finds a small set of hidden economic state processes. A feedforward network captures the non-linear effects of the conditioning variables. Our model allows us to identify the key factors that drive asset prices and generate profitable investment strategies.

Deep Arbitrage-Free Learning in a Generalized HJM Framework via Arbitrage-Regularization

“…The use of a penalty to capture no-arbitrage conditions has, to the best of the authors' knowledge, thus far only been explored numerically by Chen et al (2019) within the discrete-time portfolio optimization setting. A similar problem has been treated in Chen et al (2006) for learning the equivalent martingale measure in the multinomial tree setting for stock prices.…”

Derivatives Pricing via Machine Learning

“…Finding machine-learning based numerical methods to solve these equations is of great interest to us. Last, but not least, machine learning methods in asset pricing and portfolio optimization, which can be found in [71], [72], [73], [28], [74] and [75], admit an elegant way to price financial derivatives under  -measure. For example, we can use the method in [72] to calibrate the SDF process and use [75]…”

A General Framework of Optimal Investment

“…, i j pair. Alternative method to compute the weight process can be found in [6]. Suppose that the asset returns depend on a set of state variables, aforementioned and denoted by X.…”

“…The proposed theories prove to be effective in both simulations, in an artificial environment, and backtesting studies with real market data. Last, but not least, we propose a combination of brute-force model-free approach, such as machine learning (reinforcement learning or Q-learning) in financial analysis, which can be found in [1]- [6], and purely theoretical approaches such as no arbitrage pricing, hedging and dynamic stochastic general equilibrium (DSGE) studies. We try to find a balance between those methodologies, in order to yield better results, i.e., investment frameworks, investment management strategies and portfolio construction methodologies with good empirical performance.…”

“…Function G can depend on realized values of state variables, or conditional expected values that require us to use ANNs to predict. The ultimate output of the above optimization problem is a set of portfolio weights at each time t. Note that ω can be modeled also via ANNs, according to[6].…”