Market on a Difference

Buying one unit of $A-B$ means buying one $A$ and selling one $B$. Price the combination so that each leg trades at your own quote for that leg.

Your bid. When you buy the combination, you buy $A$ and sell $B$. Your quotes say you buy $A$ at your bid of $4$ and sell $B$ at your ask of $12$. So the combination bid is

Your ask. When you sell the combination, you sell $A$ at $5$ and buy $B$ at $10$. So the combination ask is

At these prices every combination trade is the same as two trades at your existing leg quotes. You therefore keep your edge on each leg and can lay off each leg as you would normally.

The naive market $(4-10)\ @\ (5-12) = -6\ @\ -7$ is crossed, because its bid is above its ask. That alone shows it is wrong.

The width of the correct market is $3 = 1 + 2$, the sum of the two leg widths. A spread position carries the uncertainty of both products.

Key idea. The bid of a combination is built from the price at which you would trade each leg in the direction the combination requires. For a long leg that is its bid; for a short leg it is its ask.