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


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.

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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. In humble homage to Google’s AlphaGo programme, we will refer to our double DQN algorithm as Alpha-Avellaneda-Stoikov (Alpha-AS). 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.

A Market Making Optimization Problem in a Limit Order Book

While the other parameters are kept the same as in the Table1. For the case of exponential utility function, now we explore the results of optimal controls obtained by solving the HJB Eq. Now, we display out the corresponding HJB equation of the value function .

The sought-after Q values–those corresponding to past experiences of taking actions from this state– are then computed for each of the 20 available actions, using both the prediction DQN and the target DQN (Eq ). 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. The target for the random forest classifier is simply the sign of the difference in mid-prices at the start and the end of each 5-second timestep.

High frequency trading and the new market makers

However, this would require discarding the prior avellaneda-stoikov paper of the latter every time w and k are updated, forcing the Alpha-AS models to restart their learning process every time. 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 to environment-related) values into account.

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First, we design a https://www.beaxy.com/ with variable utilities where the effects of the jumps corresponding to the orders are introduced in returns of the asset and generate optimal bid and ask prices for trading. Then, we develop another, but novel, approach considering an underlying asset model with jumps in stochastic volatility. Such an extension allows one to fit the implied volatility smile better in practice. What is common to all the above approaches is their reliance on learning agents to place buy and sell orders directly.

In , the authors present what they claim to be the first practical application of RL to optimal MM in high-frequency trading, using the LOB model proposed in to train an RL agent via simple discrete Q-Learning. The authors then demonstrate that their framework outperforms the AS and fixed-offset benchmarks. Somewhat similarly, Spooner et al. use the SARSA algorithm with a linear combination of tile codings as a value function approximator to produce an RL agent demonstrating superior out-of-sample performance across multiple securities.

2, we set the framework in continuous time and formulate the optimization problem in terms of the expected LTC return of the trader. Section3 is dedicated to the study of the stochastic control and Hamilton-Jacobi-Bellman equations for the model proposed in Sect. 3.2.1, we consider the case of the jumps in volatility of the price.

High-frequency trading and market performance

Is the value function for the control problem and, moreover, the optimal controls are given by . If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. XRP avellaneda-stoikov paper If they’ll be preparing press materials, please inform our press team within the next 48 hours.


Fortunately, the stochastic control theory helps to handle such kind of optimization problem by seeking an optimal strategy in order to maximize the trader’s objective function and to face a dyadic problem for the high-frequency trading. The theory encourages the study of optimizing activities in financial markets as it allows to accomplish the complex optimization problems involving constraints that are consistent with the price dynamics while managing the inventory risk. In order to detect the optimal quotes in the market, it is, therefore, necessary to solve the corresponding nonlinear Hamilton-Jacobi-Bellman equation for the optimal stochastic control problem. This is generally achieved by applying various root-finding algorithms that can handle the complexity and high-dimensionality of the equation. 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 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. While the other parameters are fixed to those in Table1, we see that there are more buy market orders arriving, thus the optimal filled sell spreads are larger for all inventory levels comparing to the case when the arrival of market orders is symmetric. 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.

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 . While keeping the other parameters same as in the Table1, our above expectation matches with the solutions obtained and be seen Table7. On the other hand, the results show that our strategy has a lower standard deviation. It can be also seen that the inventory of the trader reverts to zero more quickly than the symmetric strategy and the standard deviation of the inventory is produced less in the strategy.

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. The data on which the metrics for our market features were calculated correspond to one full day of trading .

  • Therefore, by choosing a Skew value the Alpha-AS agent can shift the output price upwards or downwards by up to 10%.
  • Are they scaled by some scaling parameter beforehand – and what data is this parameter estimated from ?
  • Discover a faster, simpler path to publishing in a high-quality journal.
  • The mean and the median P&L-to-MAP ratio were very significantly better for both Alpha-AS models than the Gen-AS model.


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