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<p>HVDC networks play an ever-more-significant role in today's and future power systems due to the rapid adoption of intermittent energy sources. In order to maximize the utilization of transmission grids for power systems with high share of renewable energy sources (RES) there is a need for an adequate quantification tool that is capable of accurately representing the uncertain operational characteristics of RES along with reflecting the control capabilities of HVDC converter stations. In that manner, the development of such a tool as a non-sampling one-shot mathematical structure is invaluable from the operational decision making point-of-view. This paper presents a mathematical chance-constrained framework for solving stochastic optimal power flow problem for hybrid AC/DC grids, which includes HVDC controllability and the uncertainties brought about by load and renewable energy generation, by using an intrusive general polynomial chaos approach. Three case studies are conducted on 5-bus and 67-bus hybrid AC/DC test systems to highlight the efficacy of the proposed method with a focus on the added flexibility of HVDC converters and the effects of various chance-constraint levels as well as to validate the method against Monte-Carlo simulations.</p>