Discriminant of a Quaternion Algebra over a local field

Question

I am reading Voight's "Quaternion Algebras" and I have a problem with Example 29.7.6. which is about the discriminant of a Quaternion Algebra $B$ over a local field $F/K$. The equation is $$D(B):= N(disc_{R_0}(\mathcal{O}))=N(disc_{R_0}(R))^4 N(discrd_R(\mathcal{O}))^2$$ where $N$ is the absolute norm, $\mathcal{O}$ is a maximal order, $R$ is the valuation ring of $F$ and $R_0$ is $\mathbb{Z}_p$ if $K$ is $\mathbb{Q}_p$ or $R_0=R$ otherwise and $discrd$ is the reduced discriminant. My questions are the following.

1. $disc_{R_0}(\mathcal{O})$ computed in relation to $Tr_{B/K}(\cdot)$, right?
2. Why is this equation true?

Thank you in advance.