As smart contract platforms autonomously manage billions of dollars of capital, quantifying the portfolio risk that investors engender in these systems is increasingly important. Recent work illustrates that Proof of Stake (PoS) is vulnerable to financial attacks arising from on-chain lending and has worse capital efficiency than Proof of Work (PoW) \cite{fanti_pos_econ}. Numerous methods for improving capital efficiency have been proposed that allow stakers to create fungible derivative claims on their staked assets. In this paper, we construct a unifying model for studying the security risks of these proposals. This model combines birth-death Pólya processes and risk models adapted from the credit derivatives literature to assess token inequality and return profiles. We find that there is a sharp transition between 'safe' and 'unsafe' derivative usage. Surprisingly, we find that contrary to \cite{fanti2019compounding} there exist conditions where derivatives can \emph{reduce} concentration of wealth in these networks. This model also applies to Decentralized Finance (DeFi) protocols where staked assets are used as insurance. Our theoretical results are validated using agent-based simulation.
Automated market makers, first popularized by Hanson's logarithmic market scoring rule (or LMSR) for prediction markets, have become important building blocks, called 'primitives,' for decentralized finance. A particularly useful primitive is the ability to measure the price of an asset, a problem often known as the pricing oracle problem. In this paper, we focus on the analysis of a very large class of automated market makers, called constant function market makers (or CFMMs) which includes existing popular market makers such as Uniswap, Balancer, and Curve, whose yearly transaction volume totals to billions of dollars. We give sufficient conditions such that, under fairly general assumptions, agents who interact with these constant function market makers are incentivized to correctly report the price of an asset and that they can do so in a computationally efficient way. We also derive several other useful properties that were previously not known. These include lower bounds on the total value of assets held by CFMMs and lower bounds guaranteeing that no agent can, by any set of trades, drain the reserves of assets held by a given CFMM.
This paper compares mathematical models for automated market makers including logarithmic market scoring rule (LMSR), liquidity sensitive LMSR (LS-LMSR), constant product/mean/sum, and others. It is shown that though LMSR may not be a good model for Decentralized Finance (DeFi) applications, LS-LMSR has several advantages over constant product/mean based automated market makers. However, LS-LMSR requires complicated computation (i.e., logarithm and exponentiation) and the cost function curve is concave. In certain DeFi applications, it is preferred to have computationally efficient cost functions with convex curves to conform with the principle of supply and demand. This paper proposes and analyzes constant circle/ellipse based cost functions for automated market makers. The proposed cost functions are computationally efficient (only requires multiplication and square root calculation) and have several advantages over widely deployed constant product cost functions. For example, the proposed market makers are more robust against front-runner (slippage) attacks.
David Zhao, Alessandro Rinaldo, Christopher Brookins
Few assets in financial history have been as notoriously volatile as cryptocurrencies. While the long term outlook for this asset class remains unclear, we are successful in making short term price predictions for several major crypto assets. Using historical data from July 2015 to November 2019, we develop a large number of technical indicators to capture patterns in the cryptocurrency market. We then test various classification methods to forecast short-term future price movements based on these indicators. On both PPV and NPV metrics, our classifiers do well in identifying up and down market moves over the next 1 hour. Beyond evaluating classification accuracy, we also develop a strategy for translating 1-hour-ahead class predictions into trading decisions, along with a backtester that simulates trading in a realistic environment. We find that support vector machines yield the most profitable trading strategies, which outperform the market on average for Bitcoin, Ethereum and Litecoin over the past 22 months, since January 2018.
This paper sets forth a framework for deep reinforcement learning as applied to market making (DRLMM) for cryptocurrencies. Two advanced policy gradient-based algorithms were selected as agents to interact with an environment that represents the observation space through limit order book data, and order flow arrival statistics. Within the experiment, a forward-feed neural network is used as the function approximator and two reward functions are compared. The performance of each combination of agent and reward function is evaluated by daily and average trade returns. Using this DRLMM framework, this paper demonstrates the effectiveness of deep reinforcement learning in solving stochastic inventory control challenges market makers face.
Distributed securities exchanges may become de facto fragmented if they span geographical regions with asymmetric computer infrastructure. First, we build an economic model of a decentralized exchange with two miner clusters, standing in for compact areas of economic activity (e.g., cities). "Local" miners in the area with relatively higher trading activity only join a decentralized exchange if they enjoy a large speed advantage over "long-distance" competitors. This is due to a transfer of economic value across miners, specifically from high- to low-activity clusters. Second, we estimate the speed advantage of "local" over "long-distance" miners in a series of Monte Carlo experiments over a two-cluster, unstructured peer-to-peer network simulated in C. We find that the speed advantage increases in the level of infrastructure asymmetry between clusters. Cross-region DEX blockchains are feasible as long as the asymmetry levels in trading activity and infrastructure availability across regions are positively correlated.
In order to scale transaction rates for deployment across the global web, many cryptocurrencies have deployed so-called "Layer-2" networks of private payment channels. An idealized payment network behaves like a Credit Network, a model for transactions across a network of bilateral trust relationships. Credit Networks capture many aspects of traditional currencies as well as new virtual currencies and payment mechanisms. In the traditional credit network model, if an agent defaults, every other node that trusted it is vulnerable to loss. In a cryptocurrency context, trust is manufactured by capital deposits, and thus there arises a natural tradeoff between network liquidity (i.e. the fraction of transactions that succeed) and the cost of capital deposits. In this paper, we introduce constraints that bound the total amount of loss that the rest of the network can suffer if an agent (or a set of agents) were to default - equivalently, how the network changes if agents can support limited solvency guarantees. We show that these constraints preserve the analytical structure of a credit network. Furthermore, we show that aggregate borrowing constraints greatly simplify the network structure and in the payment network context achieve the optimal tradeoff between liquidity and amount of escrowed capital.
The autonomous trading agent is one of the most actively studied areas of artificial intelligence to solve the capital market portfolio management problem. The two primary goals of the portfolio management problem are maximizing profit and restrainting risk. However, most approaches to this problem solely take account of maximizing returns. Therefore, this paper proposes a deep reinforcement learning based trading agent that can manage the portfolio considering not only profit maximization but also risk restraint. We also propose a new target policy to allow the trading agent to learn to prefer low-risk actions. The new target policy can be reflected in the update by adjusting the greediness for the optimal action through the hyper parameter. The proposed trading agent verifies the performance through the data of the cryptocurrency market. The Cryptocurrency market is the best test-ground for testing our trading agents because of the huge amount of data accumulated every minute and the market volatility is extremely large. As a experimental result, during the test period, our agents achieved a return of 1800% and provided the least risky investment strategy among the existing methods. And, another experiment shows that the agent can maintain robust generalized performance even if market volatility is large or training period is short.
This paper investigates the effects of the launch of Bitcoin futures on the intraday volatility of Bitcoin. Based on one-minute price data collected from four cryptocurrency exchanges, we first examine the change in realized volatility after the introduction of Bitcoin futures to investigate their aggregate effects on the intraday volatility of Bitcoin. We then analyze the effects in more detail utilizing the discrete Fourier transform. We show that although the Bitcoin market became more volatile immediately after the introduction of Bitcoin futures, over time it has become more stable than it was before the introduction.
We develop a model of stable assets, including non-custodial stablecoins backed by cryptocurrencies. Such stablecoins are popular methods for bootstrapping price stability within public blockchain settings. We derive fundamental results about dynamics and liquidity in stablecoin markets, demonstrate that these markets face deleveraging feedback effects that cause illiquidity during crises and exacerbate collateral drawdown, and characterize stable dynamics of the system under particular conditions. The possibility of such `deleveraging spirals' was first predicted in the initial release of our paper in 2019 and later directly observed during the `Black Thursday' crisis in Dai in 2020. From these insights, we suggest design improvements that aim to improve long-term stability. We also introduce new attacks that exploit arbitrage-like opportunities around stablecoin liquidations. Using our model, we demonstrate that these can be profitable. These attacks may induce volatility in the `stable' asset and cause perverse incentives for miners, posing risks to blockchain consensus. A variant of such attacks also later occurred during Black Thursday, taking the form of mempool manipulation to clear Dai liquidation auctions at near zero prices, costing $8m.
Juan Plazuelo Pascual, Carlos Tardon Rubio, Juan Toro Cebada, Angel Hernando Veciana
This document analyzes price discovery in cryptocurrency markets by comparing centralized and decentralized exchanges, as well as spot and futures markets. The study focuses first on Ethereum (ETH) and then applies a similar approach to Bitcoin (BTC). Chapter 1 outlines the theoretical framework, emphasizing the structural differences between centralized exchanges and decentralized finance mechanisms, especially Automated Market Makers (AMMs). It also explains how to construct an order book from a liquidity pool in a decentralized setting for comparison with centralized exchanges. Chapter 2 describes the methodological tools used: Hasbrouck's Information Share, Gonzalo and Granger's Permanent-Transitory decomposition, and the Hayashi-Yoshida estimator. These are applied to explore lead-lag dynamics, cointegration, and price discovery across market types. Chapter 3 presents the empirical analysis. For ETH, it compares price dynamics on Binance and Uniswap v2 over a one-year period, focusing on five key events in 2024. For BTC, it analyzes the relationship between spot and futures prices on the CME. The study estimates lead-lag effects and cointegration in both cases. Results show that centralized markets typically lead in ETH price discovery. In futures markets, while they tend to lead overall, high-volatility periods produce mixed outcomes. The findings have key implications for traders and institutions regarding liquidity, arbitrage, and market efficiency. Various metrics are used to benchmark the performance of modified AMMs and to understand the interaction between decentralized and centralized structures.
We study the dependency and causality structure of the cryptocurrency market investigating collective movements of both prices and social sentiment related to almost two thousand cryptocurrencies traded during the first six months of 2018. This is the first study of the whole cryptocurrency market structure. It introduces several rigorous innovative methodologies applicable to this and to several other complex systems where a large number of variables interact in a non-linear way, which is a distinctive feature of the digital economy. The analysis of the dependency structure reveals that prices are significantly correlated with sentiment. The major, most capitalised cryptocurrencies, such as bitcoin, have a central role in the price correlation network but only a marginal role in the sentiment network and in the network describing the interactions between the two. The study of the causality structure reveals a causality network that is consistently related with the correlation structures and shows that both prices cause sentiment and sentiment cause prices across currencies with the latter being stronger in size but smaller in number of significative interactions. Overall our study uncovers a complex and rich structure of interrelations where prices and sentiment influence each other both instantaneously and with lead-lag causal relations. A major finding is that minor currencies, with small capitalisation, play a crucial role in shaping the overall dependency and causality structure. Despite the high level of noise and the short time-series we verified that these networks are significant with all links statistically validated and with a structural organisation consistently reproduced across all networks.
The cryptocurrency market is a very huge market without effective supervision. It is of great importance for investors and regulators to recognize whether there are market manipulation and its manipulation patterns. This paper proposes an approach to mine the transaction networks of exchanges for answering this question. By taking the leaked transaction history of Mt. Gox Bitcoin exchange as a sample, we first divide the accounts into three categories according to its characteristic and then construct the transaction history into three graphs. Many observations and findings are obtained via analyzing the constructed graphs. To evaluate the influence of the accounts' transaction behavior on the Bitcoin exchange price, the graphs are reconstructed into series and reshaped as matrices. By using singular value decomposition (SVD) on the matrices, we identify many base networks which have a great correlation with the price fluctuation. When further analyzing the most important accounts in the base networks, plenty of market manipulation patterns are found. According to these findings, we conclude that there was serious market manipulation in Mt. Gox exchange and the cryptocurrency market must strengthen the supervision.
The blockchain technology promises to transform finance, money and even governments. However, analyses of blockchain applicability and robustness typically focus on isolated systems whose actors contribute mainly by running the consensus algorithm. Here, we highlight the importance of considering trustless platforms within the broader ecosystem that includes social and communication networks. As an example, we analyse the flash-crash observed on 21st June 2017 in the Ethereum platform and show that a major phenomenon of social coordination led to a catastrophic cascade of events across several interconnected systems. We propose the concept of ``emergent centralisation'' to describe situations where a single system becomes critically important for the functioning of the whole ecosystem, and argue that such situations are likely to become more and more frequent in interconnected socio-technical systems. We anticipate that the systemic approach we propose will have implications for future assessments of trustless systems and call for the attention of policy-makers on the fragility of our interconnected and rapidly changing world.
Célestin Coquidé, José Lages, Dima L. Shepelyansky
We construct the Google matrices of bitcoin transactions for all year quarters during the period of January 11, 2009 till April 10, 2013. During the last quarters the network size contains about 6 million users (nodes) with about 150 million transactions. From PageRank and CheiRank probabilities, analogous to trade import and export, we determine the dimensionless trade balance of each user and model the contagion propagation on the network assuming that a user goes bankrupt if its balance exceeds a certain dimensionless threshold $\kappa$. We find that the phase transition takes place for $\kappa 0.55$ almost all users remain safe. We find that even on a distance from the critical threshold $\kappa_c$ the top PageRank and CheiRank users, as a house of cards, rapidly drop to the bankruptcy. We attribute this effect to strong interconnections between these top users which we determine with the reduced Google matrix algorithm. This algorithm allows to establish efficiently the direct and indirect interactions between top PageRank users. We argue that this study models the contagion on real financial networks.
In this paper, reinforcement learning is applied to the problem of optimizing market making. A multi-agent reinforcement learning framework is used to optimally place limit orders that lead to successful trades. The framework consists of two agents. The macro-agent optimizes on making the decision to buy, sell, or hold an asset. The micro-agent optimizes on placing limit orders within the limit order book. For the context of this paper, the proposed framework is applied and studied on the Bitcoin cryptocurrency market. The goal of this paper is to show that reinforcement learning is a viable strategy that can be applied to complex problems (with complex environments) such as market making.
Abstract A blockchain replaces central counterparties with time-consuming consensus protocols to record the transfer of ownership. This settlement latency slows cross-exchange trading, exposing arbitrageurs to price risk. Off-chain settlement, instead, exposes arbitrageurs to costly default risk. We show with Bitcoin network and order book data that cross-exchange price differences coincide with periods of high settlement latency, asset flows chase arbitrage opportunities, and price differences across exchanges with low default risk are smaller. Blockchain-based trading thus faces a dilemma: Reliable consensus protocols require time-consuming settlement latency, leading to arbitrage limits. Circumventing such arbitrage costs is possible only by reinstalling trusted intermediation, which mitigates default risk.
While pump-and-dump schemes have attracted the attention of cryptocurrency observers and regulators alike, this paper represents the first detailed empirical query of pump-and-dump activities in cryptocurrency markets. We present a case study of a recent pump-and-dump event, investigate 412 pump-and-dump activities organized in Telegram channels from June 17, 2018 to February 26, 2019, and discover patterns in crypto-markets associated with pump-and-dump schemes. We then build a model that predicts the pump likelihood of all coins listed in a crypto-exchange prior to a pump. The model exhibits high precision as well as robustness, and can be used to create a simple, yet very effective trading strategy, which we empirically demonstrate can generate a return as high as 60% on small retail investments within a span of two and half months. The study provides a proof of concept for strategic crypto-trading and sheds light on the application of machine learning for crime detection.
The atomic swap protocol allows for the exchange of cryptocurrencies on different blockchains without the need to trust a third-party. However, market participants who desire to hold derivative assets such as options or futures would also benefit from trustless exchange. In this paper I propose the atomic swaption, which extends the atomic swap to allow for such exchanges. Crucially, atomic swaptions do not require the use of oracles. I also introduce the margin contract, which provides the ability to create leveraged and short positions. Lastly, I discuss how atomic swaptions may be routed on the Lightning Network.
Laura Alessandretti, Abeer ElBahrawy, Luca Maria Aiello, Andrea Baronchelli
Machine learning and AI-assisted trading have attracted growing interest for the past few years. Here, we use this approach to test the hypothesis that the inefficiency of the cryptocurrency market can be exploited to generate abnormal profits. We analyse daily data for $1,681$ cryptocurrencies for the period between Nov. 2015 and Apr. 2018. We show that simple trading strategies assisted by state-of-the-art machine learning algorithms outperform standard benchmarks. Our results show that nontrivial, but ultimately simple, algorithmic mechanisms can help anticipate the short-term evolution of the cryptocurrency market.
Attempts to accurately measure the monetary velocity or related properties of Bitcoin have often attempted to either directly apply definitions from traditional macroeconomic theory or to use specialized metrics relative to the properties of the Blockchain such as bitcoin-days destroyed. In this paper, it is demonstrated that beyond being a useful metric, bitcoin-days destroyed has mathematical properties that allow one to calculate the average dormancy (time since last use in a transaction) of the bitcoins used in transactions over a given time period. In addition, transaction volume and average dormancy are shown to have unexpected significance in helping estimate the average size of the pool of traded bitcoins by virtue of the expression Little's Law, though only under limited conditions.
In January 3, 2009, Satoshi Nakamoto gave rise to the "Bitcoin Block Chain" creating the first block of the chain hashing on his computers central processing unit (CPU). Since then, the hash calculations to mine Bitcoin have been getting more and more complex, and consequently the mining hardware evolved to adapt to this increasing difficulty. Three generations of mining hardware have followed the CPU's generation. They are GPU's, FPGA's and ASIC's generations. This work presents an agent based artificial market model of the Bitcoin mining process and of the Bitcoin transactions. The goal of this work is to model the economy of the mining process, starting from GPU's generation, the first with economic significance. The model reproduces some "stylized facts" found in real time price series and some core aspects of the mining business. In particular, the computational experiments performed are able to reproduce the unit root property, the fat tail phenomenon and the volatility clustering of Bitcoin price series. In addition, under proper assumptions, they are able to reproduce the price peak at the end of November 2013, its next fall in April 2014, the generation of Bitcoins, the hashing capability, the power consumption, and the mining hardware and electrical energy expenses of the Bitcoin network.
In standard Walrasian auctions, the price of a good is defined as the point where the supply and demand curves intersect. Since both curves are generically regular, the response to small perturbations is linearly small. However, a crucial ingredient is absent of the theory, namely transactions themselves. What happens after they occur? To answer the question, we develop a dynamic theory for supply and demand based on agents with heterogeneous beliefs. When the inter-auction time is infinitely long, the Walrasian mechanism is recovered. When transactions are allowed to happen in continuous time, a peculiar property emerges: close to the price, supply and demand vanish quadratically, which we empirically confirm on the Bitcoin. This explains why price impact in financial markets is universally observed to behave as the square root of the excess volume. The consequences are important, as they imply that the very fact of clearing the market makes prices hypersensitive to small fluctuations.
The availability of data on digital traces is growing to unprecedented sizes, but inferring actionable knowledge from large-scale data is far from being trivial. This is especially important for computational finance, where digital traces of human behavior offer a great potential to drive trading strategies. We contribute to this by providing a consistent approach that integrates various datasources in the design of algorithmic traders. This allows us to derive insights into the principles behind the profitability of our trading strategies. We illustrate our approach through the analysis of Bitcoin, a cryptocurrency known for its large price fluctuations. In our analysis, we include economic signals of volume and price of exchange for USD, adoption of the Bitcoin technology, and transaction volume of Bitcoin. We add social signals related to information search, word of mouth volume, emotional valence, and opinion polarization as expressed in tweets related to Bitcoin for more than 3 years. Our analysis reveals that increases in opinion polarization and exchange volume precede rising Bitcoin prices, and that emotional valence precedes opinion polarization and rising exchange volumes. We apply these insights to design algorithmic trading strategies for Bitcoin, reaching very high profits in less than a year. We verify this high profitability with robust statistical methods that take into account risk and trading costs, confirming the long-standing hypothesis that trading based social media sentiment has the potential to yield positive returns on investment.