A quantile regression neural network approach to estimating the conditional density of multiperiod returns

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This paper presents a new approach to estimating the conditional probability distribution of multiperiod financial returns. Estimation of the tails of the distribution is particularly important for risk management tools, such as Value-at-Risk models. A popular approach is to assume a Gaussian distribution, and to use a theoretically derived variance expression which is a non-linear function of the holding period, k, and the one-step-ahead volatility forecast, σ̂ₜ₊₁. The new method avoids the need for a distributional assumption by applying quantile regression to the historical returns from a range of different holding periods to produce quantile models which are functions of k and σ̂ₜ₊₁. A neural network is used to estimate the potentially non-linear quantile models. Using daily exchange rates, the approach is compared to GARCH-based quantile estimates. The results suggest that the new method offers a useful alternative for estimating the conditional density.