How far should a long book drag your quotes?
Asked at Optiver
You make markets in a stock worth . Flat, you'd quote / . Random flow has left you long shares, more than you'd like, and you still believe fair value is exactly .
Model your reservation price (the price you're truly indifferent to trading at) as fair value shifted by , where is your signed inventory and k = \0.00001$ per share is a risk coefficient.
Where do you center your quotes now, and what does the shift depend on?