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High-Frequency Trading Meets Online Learning Market Microstructure and Liquidity


Binary code, also known as hashing technology, is well-known for fast Hamming distance computation, less storage requirement and accurate calculation results. The Hamming space is most enjoyed by computers because of binary/hash codes. Several studies combine multi-view clustering with binary code learning for improving clustering performance. However, there is much redundant information contained in the learned binary codes, which negatively affects the clustering performance, but these studies ignore eliminating redundant information for learning compact codes. In addition, they don’t give a unified (one-step) clustering framework with binary graph structure, which doesn’t lead to the optimal clustering result due to the information loss during the two-step process.

This snapshot avellaneda & stoikov provides us with the opportunity to leverage the longer tick-time interval and make profits using machine learning algorithms. One way to improve the performance of an AS model is by tweaking the values of its constants to fit more closely the trading environment in which it is operating. In section 4.2, we describe our approach of using genetic algorithms to optimize the values of the AS model constants using trading data from the market we will operate in. Alternatively, we can resort to machine learning algorithms to adjust the AS model constants and/or its output ask and bid prices dynamically, as patterns found in market-related data evolve.


The goal with this approach is to offer a fair comparison of the former with the latter. By training with full-day backtests on real data respecting the real-time activity latencies, the models obtained are readily adaptable for use in a real market trading environment. In 2008, Avellaneda and Stoikov published a procedure to obtain bid and ask quotes for high-frequency market-making trading . The successive orders generated by this procedure maximize the expected exponential utility of the trader’s profit and loss (P&L) profile at a future time, T , for a given level of agent inventory risk aversion. In the framework of the optimal trading strategy for high-frequency trading in a LOB, there have been many papers following early studies of Grossman and Miller and Ho and Stoll . Avellaneda and Stoikov have revised the study of Ho and Stoll building a practical model that considers a single dealer trading a single stock facing with a stochastic demand modeled by a continuous time Poisson process.


Where tj is the current time upon arrival of the jth market tick, pm is the current market mid-price, I is the current size of the inventory held, γ is a constant that models the agent’s risk aversion, and σ2 is the variance of the market midprice, a measure of volatility. Table12 obtained from all simulations illustrates that the traders using the Model c have relatively higher return but also relatively a higher standard deviation comparing to other models. The performances of Sharpe ratios of each models indicates that the stock price models with stochastic volatility based on a quadratic utility function produces more attractive portfolios than the other models.

Journal of Financial Markets

And as you can see, the ask offers will be created closer to the market mid-price since the optimal spread is calculated with the reservation price as reference. Another feature of the model that you can notice in the above picture is that the reservation price is below the market mid-price in the first half of the graphic. The second part of the model is about finding the optimal position the market maker orders should be on the order book to increase profitability. If γ value is close to zero, the reservation price will be very close to the market mid-price.

It is then the latter that calculates the optimal bid and ask prices at each step. The AS model generates bid and ask quotes that aim to maximize the market maker’s P&L profile for a given level of inventory risk the agent is willing to take, relying on certain assumptions regarding the microstructure and stochastic dynamics of the market. Extensions to the AS model have been proposed, most notably the Guéant-Lehalle-Fernandez-Tapia approximation , and in a recent variation of it by Bergault et al. , which are currently used by major market making agents. Nevertheless, in practice, deviations from the model scenarios are to be expected.

What is the order book liquidity/density (κ)

Reading the paper, you won’t find any direct indication of calculating these two parameters’ values. The Avellaneda & Stoikov model was created to be used on traditional financial markets, where trading sessions have a start and an end. The inventory position is flipped, and now the bid offers are being created closer to the market mid-price. It’s easy to see how the calculated reservation price is different from the market mid-price .


An ε-greedy policy is followed to determine the action to take during the next 5-second window, choosing between exploration , with probability ε, and exploitation , with probability 1-ε. The selected action is then taken repeatedly, once every market tick, in the following 5-second window, at the end of which the reward (the Asymmetric Dampened P&L) obtained from this repeated execution of the action is computed. Where Ψ(τi) is the open P&L for the 5-second action time step, I(τi) is the inventory held by the agent and Δm(τi) is the speculative P&L (the difference between the open P&L and the close P&L), at time τi, which is the end of the ith 5-second agent action cycle. Mean decrease accuracy , a feature-specific estimate of average decrease in classification accuracy, across the tree ensemble, when the values of the feature are permuted between the samples of a test input set . To obtain MDA values we applied a random forest classifier to the dataset split in 4 folds.

While the market maker wants to maximize her profit from the transactions over a finite time horizon, she also wants to keep her inventories under control and get rid of the remaining inventories at the final time T by the penalization terms. The half-second required by the system is put to good use in practice. For a single tick, the computation time required for the main procedures is recorded in Table 8. In addition to the algorithmic calculations, we reserve time for some mechanical order-related activities, such as order submission and execution in exchanges. The Chinese A-share market can satisfy this tick-time condition with its update frequency of 3 s.

The methodology might be more sound than this, but the text simply does not offer answers to these questions. The performance of the Alpha-AS models in terms of the Sharpe, Sortino and P&L-to-MAP ratios was substantially superior to that of the Gen-AS model, which in turn was superior to that of the two standard baselines. On the other hand, the performance of the Alpha-AS models on maximum drawdown varied significantly on different test days, losing to Gen-AS on over half of them, a reflection of their greater aggressiveness, made possible by GAL their relative freedom of action.

Learning from imbalanced data

Combining a avellaneda & stoikov 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. Gašperov and Konstanjčar tackle the problem be means of an ensemble of supervised learning models that provide predictive buy/sell signals as inputs to a DRL network trained with a genetic algorithm. The same authors have recently explored the use of a soft actor-critic RL algorithm in market making, to obtain a continuous action space of spread values .

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On hummingbot, you choose what the asset inventory target is, and the bot calculates the value of q. This parameter is used to calculate what is the difference between the current inventory position and the desired one. But for now, it is essential to know that using a significant κ value, you are assuming that the order book is denser, and your optimal spread will have to be smaller since there is more competition on the market.

In Section 2, we introduce some basic concepts and describe the input LOB datasets. For every day of data the number of ticks occurring in each 5-second interval had positively skewed, long-tailed distributions. The means of these thirty-two distributions ranged from 33 to 110 ticks per 5-second interval, the standard deviations from 21 to 67, the minimums ran from 0 to 20, the maximums from 233 to 1338, and the skew ranged from 1.0 to 4.4. The prediction DQN receives as input the state-defining features, with their values normalised, and it outputs a value between 0 and 1 for each action. The DQN has two hidden layers, each with 104 neurons, all applying a ReLu activation function.

  • Closing_time – Here, you set how long each “trading session” will take.
  • The results obtained suggest avenues to explore for further improvement.
  • In order to evaluate the efficiency of RAGE, we perform experiments showing how RAGE behaves when we change the number of random solutions generated per round, and the number of candidate elements removed per round.
  • The limit bid and ask orders are canceled, and new orders are placed according to the current mid-price and spread at this interval.

The strategy will not place any orders if you do not have sufficient balance on either side of the order. We aim to teach new users the basics of market-making while enabling experienced users to exercise more control over how their bots behave. By default, when you run create, we ask you to enter the basic parameters needed for a market-making bot. Continuous-time stochastic control and optimization with financial applications. In order to recall the models easier, we call the model studied in in Case 1 in Sect. 3 with stock price dynamics as “Model 1” and the model with the dynamics “Model 2”.

  • The Asymmetric dampened P&L penalizes speculative positions, as speculative profits are not added while losses are discounted.
  • Overall, however, days of substantially better performance relative to the non-Alpha-AS models far outweigh those with poorer results, and at the end of the day the Alpha-AS models clearly achieved the best and least exposed P&L profiles.
  • Rather, taking inspiration from Teleña , we mediate the order placement decisions through the AS model (our “avatar”, taking the term from ), leveraging its ability to provide quotes that maximize profit in the ideal case.

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