Optimal Limit Order Book Trading Strategies with Stochastic Volatility in the Underlying Asset SpringerLink

Increment means that more buy market orders arrived and are filled by sell orders which causes larger spreads. For a fixed inventory level q and a representation of the asset volatility which are obtained from one simulation. Similar to the proof of Proposition2, the optimal spreads can be found by the first order optimality conditions. Is the set of the admissible strategies, F and G are the instantaneous and terminal reward functions, respectively.

The usual approach in algorithmic trading research is to use machine learning algorithms to determine the buy and sell orders directly. In contrast, we propose maintaining the Avellaneda-Stoikov procedure as the basis upon which to determine the orders to be placed. We use a reinforcement learning algorithm, a double DQN, to adjust, at each trading step, the values of the parameters that are modelled as constants in the AS procedure. The actions performed by our RL agent are the setting of the AS parameter values for the next execution cycle.

Quantitative Finance

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 combination of the choice of one from among four available values for γ, with the choice of one among five values for the skew, consequently results in 20 possible actions for the agent to choose from, each being a distinct (γ, skew) pair. We chose a discrete action space for our experiment to apply RL to manipulate AS-related parameters, aiming keep the algorithm as simple and quickly trainable as possible. A continuous action space, as the one used to choose spread values in , may possibly perform better, but the algorithm would be more complex and the training time greater. Following the approach in López de Prado , where random forests are applied to an automatic classification task, we performed a selection from among our market features , based on a random forest classifier. We did not include the 10 private features in the feature selection process, as we want our algorithms always to take these agent-related (as opposed GALA to environment-related) values into account.

Then, the model trained daily or weekly can predict trading actions and the probability of each choice at every tick. The next step is to trade the securities based on the information yielded by the predictions. Instead of investing the same proportion consistently, we devise an optimization scheme using the fractional Kelly growth criterion under risk control, which is further achieved by the risk measure, value at risk . Based on the estimates of historical VaR and returns for successful/failed actions, we provide a theoretical closed-form solution for the optimal investment proportion.

Minimum Order Size

To fill this gap, this 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. Meanwhile, interpretable results show that IIFI can effectively distinguish between important and redundant features via rating corresponding scores to each feature.

The selection of features based on these three metrics reduced their number from 112 to 22 . The features retained by each importance indicator are shown in Table 1. The ranges of possible values of the features that are defined in relation to the market mid-price, are truncated to the interval [−1, 1] (i.e., if a value exceeds 1 in magnitude, it is set to 1 if it is positive or -1 if negative).

What is the order book liquidity/density (κ)

The value of q on the formula measures how many units the market maker inventory is from the desired target. To start this override feature, users must input the parameters manually in the strategy config file they intend to use. The Volatility Sensibility will recalculate gamma, kappa, and eta after the value of volatility sensibility threshold in percentage is achieved. For example, when the parameter is set to 0, it will recalculate gamma, kappa, and eta each time an order is created. In expert mode, the user will need to directly define the algorithm’s basic parameters described in the foundation paper, and no recalculation of parameters will happen. Topics in stochastic control with applications to algorithmic trading.

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. S′ is the state the MDP has transitioned to when taking action a from state s, to which it arrived at the previous iteration. R is the latest reward obtained from state s by taking action a. Papers With Code is a free resource with all data licensed under CC-BY-SA. You can find a lot of content about market making on our Youtube Channel, including interviews with professional traders and news about cryptocurrency-related events. Cryptocurrency markets are 24/7, so there is no market closing time.

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Market indicators, consisting of features describing the state of the environment. Discover a faster, simpler path to publishing in a high-quality journal. PLOS ONE promises fair, rigorous peer review, broad scope, and wide readership – a perfect fit for your research every time. Stay informed on the latest trending ML papers with code, research developments, libraries, methods, and datasets. If you want to end the trading session with your entire inventory allocated to USDT, you set this value to 0. You will be asked the maximum and minimum spread you want hummingbot to use on the following two questions.

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. Reducing the number of features considered by the RL agent in turn dramatically reduces the number of states. This helps the algorithm learn and improves its performance by reducing latency and memory requirements.

The imprecise Dirichlet model provides workaround, by replacing point probability estimates with interval-valued ones. This paper investigates a new tree aggregation method based on the theory of belief functions to combine such probability intervals, resulting in a cautious random forest classifier. In particular, we propose a strategy for computing tree weights based on the minimization of a convex cost function, which takes both determinacy and accuracy into account and makes it possible to adjust the level of cautiousness of the model. The proposed model is evaluated on 25 UCI datasets and is demonstrated to be more adaptive to the noise in training data and to achieve a better compromise between informativeness and cautiousness.

• Recently, there have been crucial developments in quantitative financial strategies to execute the orders driven in markets by computer programs with a very high speed .
• The literature on the optimal market making problem has been burgeoning since 2008 with the work of Avellaneda and Stoikov , inspiring Guilbaud and Pham to derive a model involving limit and market orders with optimal stochastic spreads.
• It is demonstrated that the Model d has a Gaussian normal distribution while the others are positively skewed.

Conversely, test avellaneda and stoikov 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”). On the P&L-to-MAP ratio, Alpha-AS-1 was the best-performing model for 11 test days, with Alpha-AS-2 coming second on 9 of them, whereas Alpha-AS-2 was the best-performing model on P&L-to-MAP for 16 of the test days, with Alpha-AS-1 coming second on 14 of these. Here the single best-performing model was Alpha-AS-2, winning for 16 days and coming second on 10 (on 9 of which losing to Alpha-AS-1). Alpha-AS-1 had 11 victories and placed second 16 times (losing to Alpha-AS-2 on 14 of these). AS-Gen had the best P&L-to-MAP ratio only for 2 of the test days, coming second on another 4. The mean and the median P&L-to-MAP ratio were very significantly better for both Alpha-AS models than the Gen-AS model.

The figures represent the percentage of wins of one among the https://www.beaxy.com/s in each group against all the models in the other group, for the corresponding performance indicator. To perform the first genetic tuning of the baseline AS model parameters (Section 4.2). Again, the probability of selecting a specific individual for parenthood is proportional to the Sharpe ratio it has achieved.

Furthermore, considering the dynamic time-series and potentially non-stationary structure of industrial data, we propose extended incremental versions to alleviate the complexity of the overall model computation. Extensive data recovery experiments are conducted on two real industrial processes to evaluate the proposed method in comparison with existing state-of-the-art restorers. The results show that the proposed methods can impute better with different missing rates and have strong competitiveness in practical application. Reinforcement learning algorithms have been shown to be well-suited for use in high frequency trading contexts [16, 24–26, 37, 45, 46], which require low latency in placing orders together with a dynamic logic that is able to adapt to a rapidly changing environment. In the literature, reinforcement learning approaches to market making typically employ models that act directly on the agent’s order prices, without taking advantage of knowledge we may have of market behaviour or indeed findings in market-making theory.

From the negative values in the Max DD columns, we see that Alpha-AS-1 had a larger Max DD (i.e., performed worse) than Gen-AS on 16 of the 30 test days. However, on 13 of those days Alpha-AS-1 achieved a better P&L-to-MAP score than Gen-AS, substantially so in many instances. Only on one day was the trend reversed, with Gen-AS performing slightly worse than Alpha-AS-1 on Max DD, but then performing better than Alpha-AS-1 on P&L-to-MAP. This is obtained from the algorithm’s P&L, discounting the losses from speculative positions. The Asymmetric dampened P&L penalizes speculative positions, as speculative profits are not added while losses are discounted.

On this performance indicator, AS-Gen was the overall best performing model, winning on 11 days. The mean Max DD for the AS-Gen model over the entire test period was visibly the lowest , and its standard deviation was also the lowest by far from among all models. In comparison, both the mean and the standard deviation of the Max DD for the Alpha-AS models were very high. Indeed, the differences in Max DD performance between Gen-AS and either of the Alpha-AS models, over all test days, are not statistically significant, despite the large differences in means.