# Fair Value Regression Methods

Recently we had an invited talk at our university (I'm Ph.D. student in ML department, so I'm sorry if my question is stupid, since I do not have quantitative finance background), where one researcher from large market maker company was talking about what they do, and he mentioned fair value estimation for bid-ask spread as one of the problems. In his talk, he explained quite well what it is and how it is used in practice and he mentioned that "simple regression method does it quite well".

What I was wondering is, how can one use "simple regression" to regress fair value? That would assume that one can assign post-factum fair value in the dataset but I can't come up with the solution on how can one assign this value so easily and would guess that such kind of a problem would be better solved using optimal control problems.

Are there any good academic papers that deal with fair value regression and would probably answer my question?

Thanks!

Since in the data one knows $$P^b, P^a, V^b, V^a$$, i.e. best bid/ask price, and best bid/ask volume at the current time, one can consider the following definitions of fair value:
• Just a mid-price, i.e. $$P = \frac{1}{2}(P^b + P^a)$$
• Microprice (also known as weighted mid-price), i.e. $$P = \frac{V^b}{V^a + V^b}P^a + \frac{V^a}{V^b + V^a}P^b$$