Model Definition:
The Avellaneda Stoikov (A-S):
r(s,t) = s - qγσ²(T-t)
δ(t) = (2/γ)ln(1 + γ/κ) + γσ²(T-t)
Its closed-form solution yields
Optimal Quotes that
quantify
sensitivity to market microstructure: q (inventory skew), γ (risk aversion),
σ (volatility), and κ (order flow liquidity).