Abstract
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.
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