Before revision:  In this manuscript, we discuss a penalized maximum likelihood approach for estimating the conditional distribution in an SV model in a nonparametric way, thus avoiding any potentially critical assumptions on the shape  .
After revision:  In this manuscript, we discuss a penalized maximum likelihood approach for estimating the conditional distribution in an SV model in a nonparametric way, thus avoiding any potentially critical assumptions on the shape . The considered framework exploits the strengths both of the powerful hidden Markov model machinery and of penalized B-splines, and constitutes a powerful and flexible alternative to recently developed Bayesian approaches to semiparametric SV modelling. We demonstrate the feasibility of the approach in a simulation study before outlining its potential in applications to three series of returns on stocks and one series of stock index returns .