What is the meaning of "I'm covered"?

Solution 1:

Whether the writer is discussing insurance formally or not I think he (or she) is talking about actuarial risk which is what insurance companies use to calculate the chances of having to pay out against a given policy.

What the writer is saying is that if they assume that the risk of the Yellowstone volcano erupting in the next ten years is less than one percent that would be a reasonable figure to use in the calculation of the premium, in other words that the policy has a more than ninety nine percent possibility of making a profit over the ten year period. In other words that their risk is covered.

The writer is probably speaking metaphorically (ie no insurance policy is involved) but that is the background to the metaphor.

Solution 2:

Based on the context of this sentence, I would interpret it as "I'm good." or "I'm going to be safe."