We were able to achieve some parallelisation by running five backtests simultaneously on different CPU cores. Upon finalization of the five parallel backtests, the five respective memory replay buffers were merged. 10 such training iterations were completed, all on data from the same full day of trading, with the memory replay buffer resulting from each iteration fed into the next. The replay buffer obtained from the final iteration was used as the initial one for the test phase.
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.
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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. A second contribution is the setting of the initial parameters of the Avellaneda-Stoikov procedure by means of a genetic algorithm working with real backtest data. This is an efficient way of arriving at quasi-optimal values for these parameters given the market environment in which the agent begins to operate.
Data normalization for features and labeling for signals are required for classification. Instead of simply labeling the mid-price movement as in Kercheval and Zhang and Tsantekidis et al. , we consider the direct trading actions, including long, short, and none. This approach 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.
Market making models: from Avellaneda-Stoikov to Gue´ant- Lehalle, and beyond
Market making is a high-frequency trading problem for which solutions based on reinforcement learning are being explored increasingly. Two variants of the deep RL model (Alpha-AS-1 and Alpha-AS-2) were backtested on real data (L2 tick data from 30 days of bitcoin–dollar pair trading) alongside the Gen-AS model and two other baselines. The performance of the five models was recorded through four indicators (the Sharpe, Sortino and P&L-to-MAP ratios, and the maximum drawdown). Gen-AS outperformed the two other baseline models on all indicators, and in turn the two Alpha-AS models substantially outperformed Gen-AS on Sharpe, Sortino and P&L-to-MAP. 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.
This half a second enables our system, which is trained with a deep-learning architecture, to integrate price prediction, trading signal generation, and optimization for capital allocation on trading signals altogether. It also leaves sufficient time to submit and execute orders before the next tick-report. Besides, we find that the number of signals generated from the system can be used to rank stocks for the preference of LOB trading. We test the system with simulation experiments and real data from the Chinese A-share market. The simulation demonstrates the characteristics of the trading system in different market sentiments, while the empirical study with real data confirms significant profits after factoring in transaction costs and risk requirements.
To prevent it from happening, users can avellaneda stoikov the risk_factor to a lower value. The farther the current inventory is from the desired asset allocation , the greater the distance between reservation price and the market mid price. The strategy skews the probability of either buy or sell orders being filled, depending on the difference between the current inventory and the inventory_target_base_pct. In this section, we compare the existing optimal market making models based on the stock price impacts with the models that we introduce in the previous sections. Numerical experiments are carried out on two different types of utility functions, i.e., quadratic and exponential utility functions. Wireless ad hoc networks are infrastructureless networks and are used in various applications such as habitat monitoring, military surveillance, and disaster relief.
Some HFT reading. Gueant, Stoikov, and Avellaneda (yes all their papers, in that order) are mandatory reading. Try to implement a few and get some experience. Some selected papers. Adversity in cryptocurrency markets is also great (feature wise). https://t.co/gwBhgtJJiU
— Stat Arb (@quant_arb) July 4, 2022
Graph theory provides a great foundation to tackle the emerging problems in WANETs. A vertex cover is a set of vertices where every edge is incident to at least one vertex. The minimum weighted connected VC problem can be defined as finding the VC of connected nodes having the minimum total weight. MWCVC is a very suitable infrastructure for energy-efficient link monitoring and virtual backbone formation. In this paper, we propose a novel metaheuristic algorithm for MWCVC construction in WANETs.
Journal of Financial Markets
Please inspect the strategy code in Trading Logic above to understand exactly how it works.
The models underlying the AS procedure, as well as its implementations in practice, rely on certain assumptions. Statistical assumptions are made in deriving the formulas that solve the P&L maximization problem. For instance, Avellaneda and Stoikov (ibid.) illustrate their method using a power law to model market order size distribution and a logarithmic law to model the market impact of orders. Furthermore, as already mentioned, the agent’s risk aversion (γ) is modelled as constant in the AS formulas. Finally, as noted above, implementations of the AS procedure typically use the reservation price as an approximation for both the bid and ask indifference prices. 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.
Deep LOB trading: Half a second please!
Double DQN LTC is a deep RL approach, more specifically deep Q-learning, that relies on two neural networks, as we shall see shortly (in Section 4.1.7). In this paper we present a double DQN applied to the market-making decision process. Typically, in the beginning the agent does not know the transition and reward functions. It must explore actions in different states and record how the environment responds in each case.
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). The new genetic values form the chromosome of the offspring model. With the above definition of our Alpha-AS agent and its orderbook environment, states, actions and rewards, we can now revisit the reinforcement learning model introduced XRP https://www.beaxy.com/ in Section (4.1.2) and specify the Alpha-AS RL model. Γd is a discount factor (γd∈) by which future expected rewards are given less weight in the current Q-value than the latest observed reward.
- Our algorithm is a population-based iterated greedy approach that is very effective against graph theoretical problems.
- The central notion is that, by relying on a procedure developed to minimise inventory risk (the Avellaneda-Stoikov procedure) by way of prior knowledge, the RL agent can learn more quickly and effectively.
- In order to see the time evolution of the process for larger inventory bounds.
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. 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.
This consideration makes rb and ra reasonable reference prices around which to construct the market maker’s spread. Avellaneda and Stoikov define rb and ra, however, for a passive agent with no orders in the limit order book. In practice, as Avellaneda and Stoikov did in their original paper, when an agent is running and placing orders both rb and ra ra are approximated by the average of the two, r . 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. The minimum_spread parameter is optional, it has no effect on the calculated reservation price and the optimal spread.
We the market-agent interplay as a Markov Decision Process with initially unknown state transition probabilities and rewards. If users choose to set the eta parameter, order sizes will be adjusted to further optimize the strategy behavior in regards to the current and desired portfolio allocation. This value is defined by the user, and it represents how much inventory risk he is willing to take. Topics in stochastic control with applications to algorithmic trading. PhD Thesis, The London School of Economics and Political Sciences. And for the stock price dynamics which are provided in each model definition.