Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable x and a dependent variable y by modeling their conditional probability p(y|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.

@techreport{rothfuss2019conditional,
    Archiveprefix = {arXiv},
    Author = {Rothfuss, Jonas and Ferreira, Fabio and Walther, Simon and Ulrich, Maxim},
    Eprint = {1903.00954},
    Month = {March},
    Primaryclass = {stat.ML},
    Publisher = {ArXiv},
    Title = {Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks},
    Year = {2019},
}