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Hard · Market Microstructure · Quant Trader interview question · avellaneda-stoikov, market-making, inventory, optimal-pricing
You are a market maker using the Avellaneda-Stoikov model for a highly liquid stock. Your risk aversion parameter is denoted by $ \gamma $ and your inventory is denoted by $q$. The mid-price follows a Brownian motion with volatility $ \sigma $ . Time to expiry of your market making activity is $T$. How does the absolute value of the adjustment to the mid-price, used to determine your optimal bid and ask quotes, change as your inventory $q$ deviates further from zero (either positive or negati