The roll-out of stochastic renewable energy sources (RES) undermines the efficiency of power system and market operations. This paper proposes an approach to derive electricity prices that internalize RES stochasticity. We leverage a chance-constrained AC Optimal Power Flow (CC AC-OPF) model, which is robust against RES uncertainty and is also aware of the resulting variability (variance) of the system state variables. Using conic duality theory, we derive and analyze energy and balancing reserve prices that internalize the risk of system limit violations and the variance of system state variables. We compare the risk- and variance-aware prices on the IEEE 118-node testbed.