Recently, Bayesian solutions to the quantile regression problem, via the likelihood of a Skewed-Laplace distribution, have been proposed. These approaches are extended and applied to a family of dynamic conditional autoregressive quantile models. Popular Value at Risk models, used for risk management in finance, are extended to this fully nonlinear family. An adaptive Markov chain Monte Carlo scheme is designed for estimation and inference. Simulation studies illustrate favorable performance, compared to the standard numerical optimization of the usual non-parametric quantile criterion function. An empirical study employing ten major financial stock indices and Value at Risk forecasting finds significant nonlinearity in dynamic quantiles and evidence favoring the proposed model family, for lower level quantiles, compared to standard parametric volatility and risk models in the literature.