medium · Market Microstructure

Under the Avellaneda-Stoikov framework, as the maker's current inventory q grows positive (long), what happens to her optimal bid and ask quotes relative to the efficient price s, and why?

1. Both bid and ask shift DOWN by the inventory skew qγσ^2(T-t), so she quotes more aggressively to sell and more passively to buy, encouraging mean-reversion of inventory toward zero
2. Both her bid and ask quotes shift UP by qγσ^2(T-t), raising her effective offer so she captures extra spread on the side of the market she is already overexposed toward
3. The half-spread widens symmetrically by qγσ^2(T-t) around an unchanged efficient price, pricing in the larger variance risk carried by her current long inventory position
4. Only the ask quote shifts, moving down by qγσ^2(T-t), while the bid stays pinned exactly at s, since by assumption she will only ever trade to reduce, never add to, a long position

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