We present a forward-looking estimator for the time-varying physical return distribution with minimal prior assumptions about the shape of the distribution and no exogenous assumptions about the economy or preferences. Our estimator, which is based on a neural network, derives its forecasts from option-implied measures and predicts the conditional mean and volatility of returns such that profitable trading strategies can be derived. In contrast to backward-looking estimators and alternative forward-looking parametric and non-parametric approaches, its distribution forecasts cannot be rejected in statistical tests and it features lower prediction errors and higher conditional log likelihood values than the alternatives.

@article{ulrich2019forward,
  title={Forward-looking P},
  author={Ulrich, Maxim and Walther, Simon and Rothfuss, Jonas and Ferreira, Fabio},
  year={2019},
  Month = {August},
  journal = {SSRN},
}