Anna Ariadna

Author:
Pavlo Chabanov
Ukrainian Runtime Engineer
2025

1. Abstract

This document describes a high-speed cross-exchange arbitrage algorithm for cryptocurrencies that incorporates futures hedging with low leverage to protect the portfolio's USD valuation. The algorithm is developed for the STELS platform—a decentralized runtime network that seamlessly connects nodes (each linked to exchanges) and aggregates data into a distributed key-value database. The algorithm's mathematical model is managed by a recurrent neural network (RNN) that learns in real time, dynamically optimizing parameters to ensure stable USD profits while minimizing market risk.

2. Introduction

In the highly volatile cryptocurrency market, arbitrage opportunities arise from price discrepancies across different exchanges. However, without effective risk management, fluctuations in the underlying asset prices can adversely affect the overall USD valuation of a portfolio. The "Anna Ariadna" algorithm integrates an arbitrage strategy with a futures hedging mechanism, enabling compensation for adverse market movements and delivering stable profits in USD.

This algorithm is implemented on the STELS platform. STELS is a decentralized runtime network providing connectivity to global crypto markets via seamless inter-node communication, aggregating data into a distributed key-value database. Additionally, the algorithm's mathematical model is controlled by an RNN that continuously learns and adapts parameters (e.g., spread threshold, risk fraction, stop-loss, and hedging coefficient) based on real-time market data.

3. System Architecture and Diagrams

3.1. STELS Platform Architecture

Node Connectivity:
The network consists of nodes directly connected to multiple exchanges, ensuring low-latency data acquisition.
Data Aggregation:
Nodes feed market data into a distributed key-value database, synchronized across the network.
Inter-Node Communication:
Seamless communication among nodes guarantees real-time data consistency and fault tolerance.

Figure 1 (not included) would illustrate the high-level architecture, including nodes, data pipelines, and the RNN module integration.

3.2. RNN Integration

Adaptive Parameter Control:
The RNN monitors incoming market data and adjusts dynamic parameters (e.g., spread threshold $T$ , risk fraction $r$ , stop-loss $SL$ , hedging coefficient $\alpha$ ) in real time.
Learning and Optimization:
The network is continuously trained using online learning techniques and adaptive optimization algorithms.

4. Notations and Definitions

The following notations are used in the algorithm:

\begin{aligned} & i && \text{Asset index} \\ & j && \text{Exchange index} \\ & P_{ij} && \text{Price of asset } i \text{ on exchange } j \\ & P_i^{\text{min}} = \min_{j}\{P_{ij}\} && \text{Minimum price of asset } i \text{ (optimal for buying)} \\ & P_i^{\text{max}} = \max_{j}\{P_{ij}\} && \text{Maximum price of asset } i \text{ (optimal for selling)} \\ & \Delta P_i = P_i^{\text{max}} - P_i^{\text{min}} && \text{Spread for asset } i \\ & T && \text{Spread threshold for executing a trade} \\ \end{aligned}

Risk Management Parameters:

\begin{aligned} & B && \text{USD balance of the account} \\ & r && \text{Fraction of capital allocated to risk (e.g., 0.01 for 1\%)} \\ & R = r \times B && \text{Maximum risk per trade in USD} \\ & SL && \text{Relative stop-loss (e.g., 0.02 for 2\%)} \\ & V && \text{Trade volume (in asset units)} \\ \end{aligned}

Futures Hedging Parameters:

\begin{aligned} & P_f && \text{Price of the futures contract} \\ & CS && \text{Size of the standard futures contract} \\ & \alpha && \text{Hedging coefficient } (0 \leq \alpha \leq 1) \\ & N_f && \text{Number of futures contracts required for hedging} \\ & \Delta P_f && \text{Change in the futures contract price} \\ \end{aligned}

The RNN dynamically updates parameters such as $T$ , $r$ , $SL$ , and $\alpha$ based on real-time market data.

5. Algorithm Description

5.1. Detection of Arbitrage Opportunity

For each asset $i$ , the prices $\{P_{ij}\}$ across all exchanges are continuously monitored via the distributed database on the STELS platform. An arbitrage opportunity is identified if:

\Delta P_i = P_i^{\text{max}} - P_i^{\text{min}} \geq T

When this condition is met, a trade is initiated by:

Buying asset $i$ at price $P_i^{\text{min}}$ .
Selling asset $i$ at price $P_i^{\text{max}}$ .

5.2. Trade Volume Calculation with Risk Management

The maximum allowable loss per asset unit is defined as:

\text{Loss per unit} = P_i^{\text{min}} \times SL

To ensure that the total risk does not exceed $R$ , the trade volume $V$ must satisfy:

V \times (P_i^{\text{min}} \times SL) \leq R

Thus, the maximum permissible volume is given by:

V \leq \frac{R}{P_i^{\text{min}} \times SL} = \frac{r \times B}{P_i^{\text{min}} \times SL}

For maximum exposure within acceptable risk, the chosen volume is:

V = \frac{r \times B}{P_i^{\text{min}} \times SL}

5.3. Expected Profit Calculation

The profit per asset unit is:

\pi = P_i^{\text{max}} - P_i^{\text{min}}

The total expected profit (before costs) is:

\Pi = V \times \pi = V \times (P_i^{\text{max}} - P_i^{\text{min}})

5.4. Futures Hedging Mechanism

5.4.1. Exposure Calculation

The exposure $E$ is calculated as:

E = V \times P_i^{\text{min}}

5.4.2. Determination of Futures Contracts

To protect the USD valuation, the number of futures contracts is determined by:

N_f = \alpha \times \frac{E}{CS \times P_f}

Here, the coefficient $\alpha$ allows for low leverage by hedging only a portion of the exposure.

5.4.3. Impact of Hedging on Profit

For a change $\Delta P_f$ in the futures price, the impact on the hedged position is:

PnL_{\text{fut}} = N_f \times CS \times \Delta P_f

5.5. Final USD Profit Calculation

The final net profit in USD, after accounting for hedging and transaction costs, is:

\Pi_{\text{net}} = \Pi - PnL_{\text{fut}} - \text{Costs}

Or equivalently:

\Pi_{\text{net}} = V \times (P_i^{\text{max}} - P_i^{\text{min}}) - (N_f \times CS \times \Delta P_f) - \text{Costs}

The trade is executed only if $\Pi_{\text{net}} > 0$ and all operating costs are covered, ensuring a net profit in USD.

6. Formal Algorithm Outline (Pseudocode)

Inputs:

Price quotes $\{P_{ij}\}$ for each asset $i$ and exchange $j$ (sourced from the distributed database on the STELS platform).
Account balance $B$ , risk fraction $r$ , stop-loss $SL$ , spread threshold $T$ .
Futures hedging parameters: $P_f$ , $CS$ , hedging coefficient $\alpha$ .
Model parameters updated in real time by the RNN.

For each asset $i$ :

Price Acquisition:

P_i^{min} ← min_{j}{P_{ij}}
P_i^{max} ← max_{j}{P_{ij}}

Arbitrage Opportunity Check:

if (P_i^{max} - P_i^{min} < T) then exit for asset i

Trade Volume Calculation:

V ← (r × B) / (P_i^{min} × SL)

Expected Profit Calculation:

Π ← V × (P_i^{max} - P_i^{min})

Hedging:

E ← V × P_i^{min}
N_f ← α × (E / (CS × P_f))
PnL_fut ← N_f × CS × ΔP_f

Final Profit Calculation:

Π_net ← Π - PnL_fut - Costs

Decision Making:

if (Π_net > 0) then
    Execute simultaneous orders:
      Buy at price P_i^{min} (on the corresponding exchange)
      Sell at price P_i^{max} (on the corresponding exchange)
    Initiate hedging by opening N_f futures contracts

7. Performance Metrics and Testing

Latency and Throughput: Key performance indicators include data latency, order execution speed, and overall network throughput.
RNN Training Metrics: Monitor convergence, prediction accuracy, and parameter stability.
Backtesting and Simulation: Historical data simulations and pilot tests validate the algorithm's efficacy.
Scalability Tests: Stress tests demonstrate system performance under high market data loads and multi-asset trading.

8. Limitations and Assumptions

Market Conditions: Assumptions regarding liquidity and minimal slippage may not hold in all market scenarios.
Data Synchronization: The performance of the distributed key-value database is critical; any delay or inconsistency can affect trading decisions.
RNN Efficacy: The RNN's performance depends on the quality of real-time data and its ability to quickly adapt; continuous validation and refinement are required.
Operational Costs: Fees, commissions, and other costs must be accurately modeled to ensure overall profitability.

9. Risk Management and Compliance

Risk Policies: Detailed protocols for risk control, including position size limits and systematic stop-loss measures.
Security Measures: Protection of API keys, data encryption, and adherence to regulatory requirements.
Contingency Plans: Failover strategies and real-time monitoring to manage network or exchange disruptions.

10. Future Development and Scalability

Model Optimization: Continuous improvement of the RNN architecture and training algorithms.
System Expansion: Integration with additional data sources and exchanges, and potential support for new asset classes.
Enhanced Analytics: Implementation of advanced predictive analytics and additional risk metrics.
Documentation and Reporting: Regular updates and comprehensive reporting for investors and regulators.

11. Bibliography and References

Chan, E. (2009). Algorithmic Trading: Winning Strategies and Their Rationale. Wiley.
Aldridge, I. (2013). High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems. Wiley.
López de Prado, M. (2018). Advances in Financial Machine Learning. Wiley.
Hull, J. (2018). Risk Management and Financial Institutions (5th ed.). Wiley.
Ghemawat, S., Gobioff, H., & Leung, S.-T. (2003). The Google File System. SOSP '03.
Chang, F., et al. (2006). Bigtable: A Distributed Storage System for Structured Data. OSDI '06.
Krauss, C., Do, X. A., & Huck, N. (2017). Deep Neural Networks, Gradient-Boosted Trees, Random Forests: Statistical Arbitrage on the S&P 500. European Journal of Operational Research, 259(2), 689–702.
IEEE/ISO/IEC 26511:2018. Systems and Software Engineering — Requirements for Developers of User Documentation.

12. Use Cases and Integration Testing

Typical Scenarios: Examples demonstrating how the system responds under various market conditions.
Integration Tests: Detailed documentation of test cases, simulation environments, and success criteria.

13. Conclusion

The "Anna Ariadna" algorithm is a comprehensive solution for high-speed cross-exchange arbitrage with integrated futures hedging, designed to protect the USD valuation of the portfolio. Implemented on the STELS platform—a decentralized runtime network ensuring global connectivity and real-time data aggregation—the algorithm leverages an RNN for adaptive parameter optimization. This document, with its rigorous notation, detailed performance metrics, robust risk management protocols, and future scalability plans, adheres to the highest standards of professional algorithm documentation accepted in the United States.