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Let's consider there is an instrument N traded on a single venue (centralized anonymous limit orderbook). Let's say that most taker orders are tiny, therefore the one who stays at the best bid/offer gets most turnover. A market maker, who knows this, pursues the following strategy:

if inventory < X, place a buy order at the best bid + one tick
if inventory > X, place a sell order at the best ask - one tick

In such case, a manipulator might appear who can exploit the maker the following way. Let's denote:

a - best ask quote by anyone apart from the maker and the manipulator
b - best bid quote by anyone apart from the maker and the manipulator
t - price tick

Then, within a short period t, while a and b remain constant, the following can happen:

  1. The manipulator places a buy order at a-2t
  2. The maker places a buy order at a-t
  3. The manipulator sells to the maker at a-t
  4. When the maker's inventory is full, the manipulator removes its buy order and places a sell order at b+2t
  5. The maker places a sell order at b+t
  6. The manipulator closes its position at b+t with profit
  7. 1-6 repeated in a loop until the maker is run out of money

Is there a way a maker can protect itself from such manipulation? To be more percise, is there a strategy for a maker which wouldn't sacrafice much turnover for which there does not exist a strategy for a manipulator which allows to make risk-free profit by placing spoofing orders?

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In general, having an algorithm's logic based on "best bid" and "best ask" is not robust to manipulation. In general it is better to reason in term of "distance to the adjusted mid".

  • first you have your own recipe to compute the adjusted mid-price $p^*$; an basic example is to use the imbalance;
  • second you use your estimate of a fair bid-ask $\psi^*$, a simple version would be to use a moving average of the bid-ask spread, but what is better is to condition it by information (News for instance, or the intraday volatility) that you have.

Then you replace "best bid" by $p^*-\psi^*/2$ and "best ask" by $p^*+\psi^*/2$. Of course this is not totally immune to manipulation, but it requires to accept more risk to manipulate these indicators.

This is a quick recipe, the true way to do it is to use a model to place your quotes. One is proposed in Guéant, Olivier, C-A L, and Joaquin Fernandez-Tapia. "Dealing with the inventory risk: a solution to the market making problem" Mathematics and financial economics 7 (2013): 477-507. Simply because when you use a model, you estimate parameters and the resulting quotes are a mix of all these estimations. It is more difficult to manipulate the non linear transformation operated by the model.

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