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When modeling the dynamics of a market, a common assumption is that the impact of a "small" (e.g. very low percentage of daily traded volume) order on current and future observations of the market ("observations" being things one could use to determine how much of one asset you could trade for another, e.g. order book snapshots for a centralized exchange, token reserve levels for an automated market maker decentralized exchange, etc.) is almost nonexistent or nonexistent.

Among other things, this assumption then allows us to more easily use historical data for tasks such as backtesting of trading strategies as we do not have to alter the data as a result of our actions at whenever an action is taken.

What I want to know is if this is a potentially "dangerous" assumption and also what has been done to loosen this assumption since no matter how small an order is, it is still recorded in the transactions that have occurred and if those are publicly available, there is potential for situations such as other agents acting on the event of the "small" order with orders of their own that may not be so "small" in size, etc.

Would a potential remedy be to develop our models in a live environment? as in letting them forecast/trade/interact/evaluate on the actual market we're trying to model with a relatively small amount of capital in somewhat of a reinforcement learning framework? as this allows us to not need to assume how our actions might impact the marker since we see what happens in real time.

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If the assumption that a "small" order does not affect price dynamics is not false. Nevertheless, in the context of backtest, they are other aspects that cannot be neglected:

  1. During a back, one does not send one small order, but a series of "coherent" small orders. This series will impact price dynamics in the real life. You need a model (like a Hawkes model, cf Bacry, Emmanuel, Adrian Iuga, Matthieu Lasnier, and C-A L. "Market impacts and the life cycle of investors orders" Market Microstructure and Liquidity 1, no. 02 (2015): 1550009.) to take this into account.
  2. Moreover, even at the size of two consecutive small orders, if "high frequency signals" are used (like the orderbook imbalance, cf C-A L. and Eyal Neuman. "Incorporating signals into optimal trading" Finance and Stochastics 23 (2019): 275-311) the first order will probably change this signal, hence it create an "alternate future" in which the second order should be simulated, not in from of the same backtest.

They are a lot of ways to account for these effects (like C-A L., Olivier Guéant, and Julien Razafinimanana. "High-frequency simulations of an order book: a two-scale approach" Econophysics of Order-driven Markets: Proceedings of Econophys-Kolkata V (2011): 73-92. or Price Signals in Trade Execution, by Robert Almgren in 2019), and none of them is perfect. The important point is to keep enough doubts on the result you will obtain with your backtest, and to measure the "intensity" of this doubt, like the total liquidity that your simulation will remove, and at which price.

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  • $\begingroup$ Thank you very much for the detailed response and references! I will have to piece through all this. Do you think that, in addition to your referenced approachs, a reinforcement learning approach could prove fruitful in this situation as that is a natural way to model an environment that changes with the actions of an agent or do you feel that the potential overhead that can come with reinforcement learning may not be worth it? $\endgroup$
    – QMath
    Jan 14 at 17:38
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    $\begingroup$ @QMath that is another question, I understand your original question as: "I already have trading policy, how to backtest it?" that is different from Ï want to learn / parametrize a trading policy" $\endgroup$
    – lehalle
    Jan 14 at 18:50
  • $\begingroup$ fair point, and yes, that understanding of my question seems mostly correct, my question that I intended to ask was along the lines of "when developing a way to make trading decisions on a small scale, should we account for the impact of our order on future observations of the market ?" $\endgroup$
    – QMath
    Jan 14 at 22:50
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    $\begingroup$ @QMath the answer is: if your intend is to send only one order, maybe, otherwise it is more complicated. And you can have a look at the references I provided. $\endgroup$
    – lehalle
    Jan 15 at 5:12
  • $\begingroup$ Great, thank you for the answer to the follow-up, I will have to look over the rest of this, thanks again! :) $\endgroup$
    – QMath
    Jan 15 at 6:43

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