Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks
This work addresses conditional density estimation for finance, providing incremental improvements to enhance estimator quality and robustness in this domain.
The paper tackles the problem of conditional density estimation for finance applications by developing best practices for neural network estimators, including noise regularization and data normalization, and demonstrates superior performance on benchmarks with simulated and Euro Stoxx 50 data.
Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable $\mathbf{x}$ and a dependent variable $\mathbf{y}$ by modeling their conditional probability $p(\mathbf{y}|\mathbf{x})$. The paper develops best practices for conditional density estimation for finance applications with neural networks, grounded on mathematical insights and empirical evaluations. In particular, we introduce a noise regularization and data normalization scheme, alleviating problems with over-fitting, initialization and hyper-parameter sensitivity of such estimators. We compare our proposed methodology with popular semi- and non-parametric density estimators, underpin its effectiveness in various benchmarks on simulated and Euro Stoxx 50 data and show its superior performance. Our methodology allows to obtain high-quality estimators for statistical expectations of higher moments, quantiles and non-linear return transformations, with very little assumptions about the return dynamic.