A Bayesian time varying approach to risk neutral density estimation

We expand the literature of risk neutral density estimation across maturities from implied volatility curves, which are usually estimated and interpolated through cubic smoothing splines.The risk neutral densities are computed through the second derivative, which we extend through a Bayesian approach to the problem, featuring an extension to a multivariate setting across maturities and over time, a flexible estimation approach for the smoothing parameter, which is traditionally assumed common to all assets, known and fixed across maturities and time, but now potentially different between assets and maturities, and over time, and information borrowing about the implied curves and risk neutral densities not only across different option maturities, but also dynamically.