Nevertheless, the flexibility that the Alpha-AS models are given to move and stretch the bid and ask price spread entails that the Alpha-AS models can, and sometimes do, operate locally with higher risk. Overall performance is more meaningfully obtained from the other indicators (Sharpe, Sortino and P&L-to-MAP), which show that, at the end of the day, the Alpha-AS models’ strategy pays off. 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.

Their model uses market parameters such as volatility and client trading activity in response to pricing to determine the optimal choice. The market-maker has full control over the prices quoted to clients and its trading activity on external venues. The underlying fair price, which informs client bids, is modelled as a Brownian motion and is influenced by market impact. Figure3 depicts one simulation of the profit and loss function of the market maker at any time t during the trading session in the left panel. The profit and loss performance of the trading is displayed by the cash level histogram in the left panel.

1 Results with the quadratic utility function

Through repeated exploration the agent gradually learns the relationships between states, actions and rewards. It can then start exploiting this knowledge to apply an action selection policy that takes it closer to achieving its reward maximization goal. However, I do not see any specification of bounds for this reservation price and therefore I think there is no guarantee that ask prices computed by the market-maker will be higher or bid prices will be lower than the current price of the process. The original Avellaneda-Stoikov model was designed to be used for market making on stock markets, which have defined trading hours. The assumption was that the market maker wants to end the trading day with the same inventory he started. For example, If the strategy needs an asset to be sold to reach the inventory_target_base_pct value, sell orders will be placed closer to the mid price than buy orders.

This Avellaneda-Stoikov baseline model (Gen-AS) constitutes another original contribution, to our knowledge, in that its parameters are optimised using a genetic algorithm working on a day’s worth of data prior to the test data. The genetic algorithm selects the best-performing values found for the Gen-AS parameters on the corresponding day of data. This procedure helps establish AS parameter values that fit initial market conditions. The same set of parameters obtained for the Gen-AS model are used to specify the initial Alpha-AS models. The goal with this approach is to offer a fair comparison of the former with the latter.

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. With these values, the AS model will determine the next reservation price and spread to use for the following orders. In other words, we do not entrust the entire order placement decision process to the RL algorithm, learning through blind trial and error. 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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It serves as a hard limit below which orders won’t be placed, if users choose to ensure that buy and sell orders won’t be placed too close to each other, which may be detrimental to the market maker’s earned fees. The minimum spread is given by the minimum_spread parameter as a percentage of the mid price. By default its value is 0, therefore the strategy places orders at optimal bid and ask prices. 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. It is demonstrated that the Model d has a Gaussian normal distribution while the others are positively skewed.

We explain the idea of the algorithm and illustrate its operation through sample examples. We implement the proposed algorithm with its competitors on a widely used dataset. From extensive measurements, we obtain that the algorithm produces WCVC with less weight at the same time its monitor count and time performances are reasonable.

Market-makers, but Barzykin says the “qualitative understanding is of no less value – the model clearly answers the dilemma of whether to hedge or not to hedge”. And for the stock price dynamics which are provided in each model definition. While we do not change the rest of the parameters in Table1 and we observe our expectations in solutions which can be tracked by Table8, in coherence with .

We relied on 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.

Please inspect the strategy code in Trading Logic above to understand exactly how it works. 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. This article will simplify what each of these formulas and values means.

That is, they achieve a better P&L profile with less exposure to market movements. 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”). 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).

The limit bid and ask orders are canceled, and new orders are placed according to the current mid-price and spread at this interval. 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. 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.

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. The strategy calculates the reservation price and the optimal spread based on measurements of the current asset volatility and the order book liquidity. The asset volatility estimator is implemented as the instant_volatility indicator, the order book liquidity estimator is implemented as the trading_intensity indicator.

Post-hoc Mann-Whitney tests were conducted to analyse selected pairwise differences between the avellaneda stoikov market makings regarding these performance indicators. Table 6 compares the results of the Alpha-AS models, combined, against the two baseline models and Gen-AS. The figures represent the percentage of wins of one among the models in each group against all the models in the other group, for the corresponding performance indicator. To start filling Alpha-AS memory replay buffer and training the model (Section 5.2). Therefore, by choosing a Skew value the Alpha-AS agent can shift the output price upwards or downwards by up to 10%.

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. A single parent individual is selected randomly from the current population , with a selection probability proportional to the Sharpe score it has achieved (thus, higher-scoring individuals have a greater probability of passing on their genes). The chromosome of the selected individual is then extracted and a truncated Gaussian noise is applied to its genes (truncated, so that the resulting values don’t fall outside the defined intervals).

• In order to see the time evolution of the process for larger inventory bounds.
• For the case of a quadratic utility function, we derive the optimal spreads for limit orders and observe their behaviors.
• 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 .
• Trading strategy with stochastic volatility in a limit order book market.
• However, adding secure points to a WANET can be costly in terms of price and time, so minimizing the number of secure points is of utmost importance.
• Lastly, we compare the models that we have derived in this paper with existing optimal market making models in the literature under both quadratic and exponential utility functions.

In such context, fuzzy numbers have been suggested as a way to recode Likert-type variables. Fuzzy numbers are avellaneda stoikov market making by a membership function whose form is usually determined by an expert. In practice, researchers usually define one membership function for each Likert-type scale, not considering the peculiar characteristics of neither questions nor respondents. In this way, the individual uncertainty against each question is considered equal and constant. To overcome this limitation and to reduce the expert’s subjectivity, in this study an adaptive membership function based on CUB model is suggested to pre-transform Likert-type variables into fuzzy numbers before the adoption of a clustering algorithm.

• Papers With Code is a free resource with all data licensed under CC-BY-SA.
• These models, therefore, must learn everything about the problem at hand, and the learning curve is steeper and slower to surmount than if relevant available knowledge were to be leveraged to guide them.
• Vol_to_spread_multiplier will act as a threshold value to override max_spread when volatility is a higher value.
• But traders have little more than their judgment and experience to go by.

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. Market indicators, consisting of features describing NEAR the state of the environment.

This https://www.beaxy.com/ is inspired by the previous application of deep learning to trade signals in the context of VIX futures (Avellaneda et al., 2021). The signals are determined by the approximate wealth changes during a fixed and limited holding period, during which we set stop-loss and take-profit points. These settings are heterogeneous for different stocks, and we provide a method to assign the values of these hyperparameters based on the historical average ratio of the best ask to the best bid price. Furthermore, the threshold of signals can be adjusted according to investors’ risk aversion. This type of labeling closely reflects actual transactions and earnings.

They have considered a constant price impact using the same counting processes for both arrival and filled limit orders. More recently, Baldacci et al. have studied the optimal control problem for an option market maker with Heston model in an underlying asset using the vega approximation for the portfolio. For more developments in optimal market making literature, we refer the reader to Guéant , Ahuja et al. , Cartea et al. , Guéant and Lehalle , Nyström and Guéant et al. . In electronic markets, any trader can become a market maker who provides the liquidity to the markets in Limit Order Books ; and market makers are allowed to submit the orders on both buy and sell sides of the market by the trading mechanisms. Deciding for the best bid and ask prices that a market maker sets up is a hard and complex problem in many aspects due to the fact that the problem should be tackled as a combined problem of the modeling the asset price dynamics and the optimal spreads.