Cycles does render caustics. But since the light is traced from the camera to the lights the probability that caustics are rendered is very low. When they are rendered most people call them fireflies or noise.
That's why the
Filter Glossy in the
Caustics tab is set to 1 most of the time.
When you set it to a low value (or even zero) you will see the noisy caustics.
To fix the noise you now have the option to:
- Use an extreme high number of samples
- Turn up
- Turn on denoising in the Layers context
So Cycles is capable of rendering caustics but they will always be very noisy.
Edit: the example above is rendered with 10000 samples, 0.5 Filter Glossy and 2px denoising.
Edit 2: It also can help to set the clamping of the direct and indirect light. This will reduce the noise of caustics but also make them less bright.
This example uses a different IOR but you can see by setting clamping of the light fireflies are less visible.