However, existing methods fail to achieve both the two goals simultaneously. To fill this gap, this paper presents an interpretable intuitionistic fuzzy inference model, dubbed as IIFI. While retaining the prediction accuracy, the interpretable module in IIFI can automatically calculate the feature contribution based on the intuitionistic fuzzy set, which provides high interpretability of the model. Also, most of the existing training algorithms, such as LightGBM, XGBoost, DNN, Stacking, etc, can be embedded in the inference module of our proposed model and achieve better prediction results. The back-test experiment on China’s A-share market shows that IIFI achieves superior performance — the stock profitability can be increased by more than 20% over the baseline methods.

• The max_order_age parameter allows you to set a specific duration when resetting your order’s age.
• Conversely, test days for which the Alpha-ASs did worse than Gen-AS on P&L-to-MAP in spite of performing better on Max DD are highlighted in red (Alpha-AS “worse”).
• The models underlying the AS procedure, as well as its implementations in practice, rely on certain assumptions.
• The cumulative profit resulting from a market maker’s operations comes from the successive execution of trades on both sides of the spread.

Some of these will most likely be handled by the editorial team, but the extent of the errors is too large, evidently due to the revisions made by authors being mostly superficial. PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. So, the concepts and principles demonstrated by the model are the same, but the real world is a lot more detailed and messy. Like using walrasian auctions to teach microeconomic concepts, it seems like a nice model that’s abstracted away from the messiness of reality to make it easier to discuss, teach, or prove fundamental principles and ideas. The differences really depend on how/where the the model is used, so we often make different simplifying assumptions in our models that arguably make them more distinct from or similar to the model you cited.

3 Test models and performance indicators

And then we show how to incorporate those tiers into the model,” says Barzykin. In the paper, clients are divided into two tiers based on their sensitivity to price changes. Some clients need to take certain positions, and their activity is less likely to be influenced by changes in price, while others are more likely to trade when they see an attractive price.

So, if T is high enough, each avellaneda-stoikov in which q is not zero, the reservation price could be too high , and so the election of bid and ask quotes (both above or below the mid-price). @RRG Right, this makes sense that the market-maker can place quotes improving on the current midprice. So I guess the fact that the plot in the original paper does not show crossing between the quotes of the market-maker and the midprice is just a matter of coincidence.

Robust Market Making via Adversarial Reinforcement Learning

For even moderately large numbers of states and https://www.beaxy.com/s, let alone when the state space is practically continuous , it becomes computationally prohibitive to maintain a Qs,a matrix and iteratively to get the values contained in it to converge to the optimal Q-value estimates. To overcome this problem, a deep Q-network approximates the Qs,a matrix using a deep neural network. The DQN computes an approximation of the Q-values as a function, Q(s, a, θ), of a parameter vector, θ, of tractable size.

Finally, we demonstrate the significance of this novel system in multiple experiments. We relied on ETH random forests to filter state-defining features based on their importance according to three indicators. Various techniques are worth exploring in future work for this purpose, such as PCA, Autoencoders, Shapley values or Cluster Feature Importance . Other modifications to the neural network architectures presented here may prove advantageous.

• The mean and the median of the Sharpe ratio over all test days was better for both Alpha-AS models than for the Gen-AS model , and in turn the Gen-AS model performed significantly better on Sharpe than the two non-AS baselines.
• By internalising risk, rather than hedging on external venues, dealers can avoid crossing spreads and paying brokerage fees.
• If not, how much data is lost by only using the price differences with absolute values smaller than 1?

This article will explain the idea behind the classic paper released by Marco Avellaneda and Sasha Stoikov in 2008 and how we implemented it in Hummingbot.

Found 2 papers, 1 papers with code

Localised excessive risk-taking by the Alpha-AS models, as reflected in a few heavy dropdowns, is a source of concern for which possible solutions are discussed. In most of the many applications of RL to trading, the purpose is to create or to clear an asset inventory. DRL has been used generally to determine the actions of placing bid and ask quotes directly [23–26], that is, to decide when to place a buy or sell order and at what price, without relying on the AS model. Spooner proposed a RL system in which the agent could choose from a set of 10 spread sizes on the buy and the sell side, with the asymmetric dampened P&L as the reward function (instead of the plain P&L). Combining a deep Q-network (see Section 4.1.7) with a convolutional neural network , Juchli achieved improved performance over previous benchmarks. Kumar , who uses Spooner’s RL algorithm as a benchmark, proposes using deep recurrent Q-networks as an improved alternative to DQNs for a time-series data environment such as trading.

You will be asked the maximum and minimum spread you want hummingbot to use on the following two questions. It’s easy to see how the calculated reservation price is different from the market mid-price . On the other hand, using a smaller κ, you are assuming the order book has low liquidity, and you can use a more extensive spread. In that case, the original article is easy to find on a quick internet search, or you can find the original publication here.

These formulas have fixed parameters to model the market maker’s aversion to risk and the statistical properties of market orders. The main contribution of this paper is a new integral deep LOB trading system that embraces model training, prediction, and optimization. Inspired by the model architecture in Zhang et al., 2018, Zhang et al., 2019, we adopt the deep convolutional neural network model, which has a structure of convolutional layers and includes an inception module and LSTM module.

Papers With Code is a free resource with all data licensed under CC-BY-SA. We tested two variants of our Alpha-AS model, differing in the architecture of their hidden layers. Initial tests with a DNN featuring two dense hidden layers were followed by tests using a RNN with two LSTM (long short-term memory) hidden layers, encouraged by results reported using this architecture . This is obtained from the algorithm’s P&L, discounting the losses from speculative positions.

Avellaneda -Stoikov market making model

Mean decrease impurity , a feature-specific measure of the mean reduction of weighted impurity over all the nodes in the tree ensemble that partition the data samples according to the values of that feature . Where the 0 subscript denotes the best orderbook price level on the ask and on the bid side, i.e., the price levels of the lowest ask and of the highest bid, respectively. A discount factor (γ) by which future rewards are given less weight than more immediate ones when estimating the value of an action (an action’s value is its relative worth in terms of the maximization of the cumulative reward at termination time).

Values that are very large can have a disproportionately strong influence on the statistical normalisation of all values prior to being inputted to the neural networks. By trimming the values to the [−1, 1] interval we limit the influence of this minority of values. The price to pay is a diminished nuance in the learning from very large values, while retaining a higher sensitivity for the majority, which are much smaller. By truncating we also limit potentially spurious effects of noise in the data, which can be particularly acute with cryptocurrency data. These successes with games have attracted attention from other areas, including finance and algorithmic trading.

This helps the algorithm learn and improves its performance by reducing latency and memory requirements. Private indicators, consisting of features describing the state of the agent. Thus, the DQN approximates a Q-learning function by outputting for each input state, s, a vector of Q-values, which is equivalent to checking the row for s in a Qs,a matrix to obtain the Q-value for each action from that state. Α is the learning rate (α∈), which reduces to a fraction the amount of change that is applied to Qi from the MATIC avellaneda-stoikov observation of the latest reward and the expectation of optimal future rewards. This limits the influence of a single observation on the Q-value to which it contributes. Optimal strategies for market makers have been studied by academic researchers for a very long time now, with Thomas Ho and Hans Stoll starting to write about market dealers dynamics in 1980.

As stated in Section 4.1.7, these values for w and k are taken as the fixed parameter values for the Alpha-AS models. They are not recalibrated periodically for the Gen-AS so that their values do not differ from those used throughout the experiment in the Alpha-AS models. If w and k were different for Gen-AS and Alpha-AS, it would be hard to discern whether observed differences in the performance of the models are due to the action modifications learnt by the RL algorithm or simply the result of differing parameter optimisation values. Alternatively, w and k could be recalibrated periodically for the Gen-AS model and the new values introduced into the Alpha-AS models as well. However, this would require discarding the prior training of the latter every time w and k are updated, forcing the Alpha-AS models to restart their learning process every time.

The DQN has two hidden layers, each with 104 neurons, all applying a ReLu activation function. At the start of every 5-second time step, the latest state (as defined in Section 4.1.4) is fed as input to the prediction DQN. The sought-after Q values–those corresponding to past experiences of taking actions from this state– are then computed for each of the 20 available actions, using both the prediction DQN and the target DQN (Eq ). The data on which the metrics for our market features were calculated correspond to one full day of trading .

The Alpha-AS agent records the new market tick information by modifying the appropriate market features it keeps as part of its state representation. The agent also places one bid and one ask order in response to every tick. Once every 5 seconds, the agent records the asymmetric dampened P&L it has obtained as its reward for placing these bid and ask orders during the latest 5-second time step. Based on the market state and the agent’s private indicators (i.e., its latest inventory levels and rewards), a prediction neural network outputs an action to take. As defined above, this action consists in setting the value of the risk aversion parameter, γ, in the Avellaneda-Stoikov formula to calculate the bid and ask prices, and the skew to be applied to these. The agent will place orders at the resulting skewed bid and ask prices, once every market tick during the next 5-second time step.

The literature on machine learning approaches to market making is extensive. Nevertheless, it is still interesting to note that AS-Gen performs much better on this indicator than on the others, relative to the Alpha-AS models. This means that, provided its parameter values describe the market environment closely enough, the pure AS model is guaranteed to output the bid and ask prices that minimise inventory risk, and any deviation from this strategy will entail a greater risk. Throughout a full day of trading, it is more likely than within shorter time frames that there will be intervals at which the market is indeed closely matched by the AS formula parameters. The greater inventory risk taken by the Alpha-AS models during such intervals can be punished with greater losses.