Simplified Avellaneda-Stoikov Market Making by Crypto Chassis Open Crypto Trading Initiative

Is the value function for the control problem and, moreover, the optimal controls are given by . Papers With Code is a free resource with all data licensed under CC-BY-SA. If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact.

The market microstructure, which can be stated as the research on the strong trading mechanisms managed for the financial securities, has been equipped with the contributions by the books Hasbrouck and O’Hara . The question of the truncation of the interval of possible state feature values remains open, or there seems to be some misunderstanding between the authors and the reviewer. For instance, how are market prices (or actually differences to the mid-price) truncated to the interval [-1,1]? Are they scaled by some scaling parameter beforehand – and what data is this parameter estimated from ? If not, how much data is lost by only using the price differences with absolute values smaller than 1?

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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.

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. 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 first chart shows price, indiference price and bid, ask quotes evolution.

Optimal high-frequency trading with limit and market orders

The goal of this https://www.beaxy.com/ is first to propose an optimal quoting strategy that is adopted by the stochastic volatility, drift effect and market impact by the amount and type of the orders in the price dynamics. We also consider the case of the market impact occuring by the jumps in volatility dynamics. We derive the closed-form solutions for the optimal quotes and solve the corresponding nonlinear HJB equations using the finite difference discretization method which enables us to evaluate the spread values and derive the various simulation analyzes. Furthermore, we explore the risk and normality testings of the models depending on their strategies.

Clients also benefit, as internalisation reduces market impact. But when volatility rises and client flows become one-sided, market-makers must quickly pivot to external venues to hedge their risks. Whether to skew prices and wait for offsetting client flow, or hedge with other dealers in the open market, is a decision that is usually left to traders. But traders have little more than their judgment and experience to go by. This potential weakness of the analytical AS approach notwithstanding, we believe the theoretical optimality of its output approximations is not to be undervalued.

Cricket teams are ranked to indicate their supremacy over their counter peers in order to get precedence. Various authors have proposed different statistical techniques in cricketing works to evaluate teams. However, it does not work well to realize the consistency of the teams’ performance. With this aim, effective features are constructed for evaluating bowling and batting precedence of teams with others. Eventually, these features are integrated to formulate the Consistency Index Rank to rank cricket teams.

This strategy implements a market making strategy described in the classic paper High-frequency Trading in a Limit Order Book written by Marco Avellaneda and Sasha Stoikov. It allows users to directly adjust the risk_factor parameter described in the paper. It also features an order book liquidity estimator calculating the trading intensity parameters automatically. Additionally, the strategy implements an order size adjustment algorithm and its order_amount_shape_factor parameter as described in Optimal High-Frequency Market Making. The strategy is implemented to be used either in fixed timeframes or to be ran indefinitely.

max_spread

We study optimal trading strategy of a market maker with stock inventory in the presence of short-term market changes, especially changes in trading intensity of market participants and stock volatility. We employ Poisson jump processes in modelling such market condition changes. We provide closed form optimal bidding and asking strategies of the market maker, and analyze the market maker’s inventory changes accordingly.

Continuous-time stochastic control and optimization with financial applications. Optimal dealer pricing under transactions and return uncertainty. Risk metrics and fine tuning of high frequency trading strategies. That is introduced by Avellaneda and Stoikov and handled by quadratic approximation approach..

2 Results with the exponential utility function

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. Inventory management is therefore central to market making strategies , and particularly important in high-frequency algorithmic trading. In an influential paper , Avellaneda and Stoikov expounded a strategy addressing market maker inventory risk.

• By internalising risk, rather than hedging on external venues, dealers can avoid crossing spreads and paying brokerage fees.
• Overall, both Alpha-AS models obtain higher and more stable returns, as well as a better P&L-to-inventory profile than AS-Gen and the non-AS baseline models.
• 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. .
• The results indicate that the proposed ranking methods yield quite more encouraging insights than the recent state-of-the-art works and can be acquired for ranking cricket teams.
• It must explore actions in different states and record how the environment responds in each case.

At this point the trained neural network model had 10,000 rows of experiences and was ready to be tested out-of-sample against the baseline AS models. As we shall see shortly, the reward function is the Asymmetric dampened P&L obtained in the current 5-second time step. In contrast, the total P&L accrued so far in the day is what has been added to the agent’s state space, since it is reasonable for this value to affect the agent’s assessment of risk, and hence also how it manipulates its risk aversion as part of its ongoing actions. Together, a) and b) result in a set of 2×10d contiguous buckets of width 10−d, ranging from −1 to 1, for each of the features defined in relative terms. Approximately 80% of their values lie in the interval [−0.1, 0.1], while roughly 10% lie outside the [−1, 1] interval. 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.

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. 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). Before any estimates can be given, both estimators need to have their buffers filled. By default the lengths of these buffers are set to be 200 ticks. In case of the trading_intensity estimator only order book snapshots different from preceding snapshots count as valid ticks.

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. However, because of the characteristics of imbalanced classification, we replace the categorical cross-entropy loss function with the focal loss function. It is necessary to pay more attention on the minority cases and capture the patterns of these valuable long and short signals. 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 .

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Finally, the best-performing model overall, with its corresponding parameter values contained in its chromosome, is retained for subsequent application to the problem at hand. In our case, it will be the AS model used as a baseline against which to compare the performance of our Alpha-AS model. The Avellaneda-Stoikov procedure underpinning the market-making actions in the models under discussion is explained in Section 2. Section 3 provides an overview of reinforcement learning and its uses in algorithmic trading. The deep reinforcement learning models (Alpha-AS-1 and Alpha-AS-2) developed to work with the Avellaneda-Stoikov algorithm are presented in detail in Section 4, together with an Avellaneda-Stoikov model (Gen-AS) without RL with parameters obtained with a genetic algorithm. Section 5 describes the experimental setup for backtests that were performed on our RL models, the Gen-AS model and two simple baselines.

• Before any estimates can be given, both estimators need to have their buffers filled.
• As a byproduct of our interpretable methods, the scores over features can be used to further optimize the investment strategy.
• Figures in bold are the best values among the five models for the corresponding test days.
• When parameters are closer to 0, spreads will be almost symmetrical.
• This article will simplify what each of these formulas and values means.

Market makers tend to do better in mean-reverting environments, whereas market momentum, in either direction, hurts their performance. To prevent it from happening, users can set the risk_factor to a lower value. In a paper published on Risk.net earlier this month, they define the choice between internalisation and externalisation as an optimisation problem in which the state variable is the inventory of the market-maker.

Nevertheless, in practice, deviations from the model scenarios are to be expected. Under real trading conditions, therefore, there is room for improvement upon the orders generated by the closed-form AS model and its variants. If more than 1 order_levels are chosen, multiple buy and sell limit orders will be created on both sides, with predefined price distances from each other, with the levels closest to the reservation price being set to the optimal bid and ask prices. This price distance between levels is defined as a percentage of the optimal spread calculated by the strategy. Given that optimal spreads tend to be tight, the level_distances values should be in general in tens or hundreds of percents.

It is directly proportional to the asymmetry between the avellaneda stoikov market making and ask spread. The Avellaneda Market Making Strategy is designed to scale inventory and keep it at a specific target that a user defines it with. To achieve this, the strategy will optimize both bid and ask spreads and their order amount to maximize profitability. The results obtained suggest avenues to explore for further improvement. First, the reward function can be tweaked to penalise drawdowns more directly.

Whether to enable adding transaction costs to order price calculation. When placing orders, if the order’s size determined by the order price and quantity is below the exchange’s minimum order size, then the orders will not be created. You will need to hold a sufficient inventory of quote and or base currencies on the exchange to place orders of the exchange’s minimum order size. No significant differences were found between the two Alpha-AS models. Single feature importance , an out-of-sample estimator of the individual importance of each feature, that avoids the substitution effect found with MDI and MDA .