DeFOx

Technology is reshaping the future of the financial landscape and challenging traditional stakeholders. The aim of DeFOx is to discuss and promote academic and industrial work addressing the emerging challenges in finance. DeFOx focuses the attention on the recent and cutting-edge contributions to topics in decentralised finance and financial technology: economics, microstructure, models of liquidity taking and making, and new design paradigms that can help lay the foundations for the future financial landscape.

Future Talks

(Online) November 1, 2023
Yiming Ma (Columbia University, Columbia Business School)
Stablecoin Runs and the Centralization of Arbitrage Link to paper
Abstract We analyze the run risk of USD-backed stablecoins. Stablecoin issuers aim to keep the stablecoin price at $1 by holding a portfolio of US dollar assets like bank deposits, Treasuries, and corporate bonds while promising to exchange stablecoins for $1 in cash with arbitrageurs. We show that asset illiquidity coupled with fixed redemption values reinstates panic runs among investors that only trade stablecoins in secondary markets with flexible prices. Importantly, run risk is exacerbated by more efficient arbitrage, implying a tradeoff between price stability and run risk. This is why stablecoin issuers only authorize a concentrated set of arbitrageurs despite the cost to price stability. Our findings are based on a model calibrated with a novel dataset on stablecoin arbitrage and trading activity. Our model predicts economically significant run risk for Tether (USDT) due to its liquidity transformation. But run risk is also sizeable for Circle (USDC) due to its less concentrated arbitrage. Finally, we show that issuing dividends to investors would effectively reduce run risk at both USDT and USDC, which points to a potential benefit of regulating stablecoins as securities.

Bio: Yiming Ma is an Associate Professor of Finance at Columbia Business School. She is interested in understanding the evolving landscape of financial intermediation, where non-banks like mutual funds and ETFs are increasingly engaged in liquidity transformation while the traditional banking sector is transforming less liquidity than before. She studies the implications of this trend on asset prices, financial stability, and monetary policy transmission. Her work applies a combination of theoretical and empirical methods. In particular, She uses structural estimation to consider how the competition and trading between financial institutions affect aggregate outcomes.
(Online) November 8, 2023
Guillermo Angeris (Bain Capital Crypto)
The Geometry of Constant Function Market Makers Link to paper
Abstract Constant function market makers (CFMMs) are the most popular type of decentralized trading venue for cryptocurrency tokens. In this paper, we give a very general geometric framework (or 'axioms') which encompass and generalize many of the known results for CFMMs in the literature, without requiring strong conditions such as differentiability or homogeneity. One particular consequence of this framework is that every CFMM has a (unique) canonical trading function that is nondecreasing, concave, and homogeneous, showing that many results known only for homogeneous trading functions are actually fully general. We also show that CFMMs satisfy a number of intuitive and geometric composition rules, and give a new proof, via conic duality, of the equivalence of the portfolio value function and the trading function. Many results are extended to the general setting where the CFMM is not assumed to be path-independent, but only one trade is allowed. Finally, we show that all 'path-independent' CFMMs have a simple geometric description that does not depend on any notion of a 'trading history'.

Bio: Head of research at Bain Capital Crypto. During his Ph.D. (2019-2022) Guille worked on inverse design in the Nanoscale and Quantum Photonics lab with Prof. Jelena Vučković and Prof. Stephen Boyd. His thesis, Heuristics and bounds for photonic design, focused mostly on some applications of optimization to photonics. He also did his bachelor's and master's at Stanford, also in EE.
(Online) November 22, 2023
Haochen Zhang (UCLA)
Adaptive Liquidity Provision in Uniswap V3 with Deep Reinforcement Learning Link to paper
Abstract Decentralized exchanges (DEXs) are a cornerstone of decentralized finance (DeFi), allowing users to trade cryptocurrencies without the need for third-party authorization. Investors are incentivized to deposit assets into liquidity pools, against which users can trade directly, while paying fees to liquidity providers (LPs). However, a number of unresolved issues related to capital efficiency and market risk hinder DeFi's further development. Uniswap V3, a leading and groundbreaking DEX project, addresses capital efficiency by enabling LPs to concentrate their liquidity within specific price ranges for deposited assets. Nevertheless, this approach exacerbates market risk, as LPs earn trading fees only when asset prices are within these predetermined brackets. To mitigate this issue, this paper introduces a deep reinforcement learning (DRL) solution designed to adaptively adjust these price ranges, maximizing profits and mitigating market risks. Our approach also neutralizes price-change risks by hedging the liquidity position through a rebalancing portfolio in a centralized futures exchange. The DRL policy aims to optimize trading fees earned by LPs against associated costs, such as gas fees and hedging expenses, which is referred to as loss-versus-rebalancing (LVR). Using simulations with a profit-and-loss (PnL) benchmark, our method demonstrates superior performance in ETH/USDC and ETH/USDT pools compared to existing baselines. We believe that this strategy not only offers investors a valuable asset management tool but also introduces a new incentive mechanism for DEX designers.

Bio: Haochen Zhang completed his Bachelor of Engineering degree in Electrical Engineering from Chongqing University in 2022. Since 2022, he has been pursuing a Master’s degree in Electrical and Computer Engineering at University of California Los Angeles (UCLA) in Los Angeles, CA, USA. He is working with Professor Lin F. Yang on reinforcement learning and its application in decentralized finance.

Past Talks

(Online) October 11, 2023
Mohak Goyal (Stanford University)
Optimal Design of Constant Function Market Makers Link to paper
Abstract Constant Function Market Makers (CFMMs) are a tool for creating exchange markets, have been deployed effectively in prediction markets, and are now especially prominent in the Decentralized Finance ecosystem. We show that for any set of beliefs about future asset prices, an optimal CFMM trading function exists that maximizes the fraction of trades that a CFMM can settle. We formulate a convex program to compute this optimal trading function. This program, therefore, gives a tractable framework for market-makers to compile their belief function on the future prices of the underlying assets into the trading function of a maximally capital-efficient CFMM. Our convex optimization framework further extends to capture the tradeoffs between fee revenue, arbitrage loss, and opportunity costs of liquidity providers. Analyzing the program shows how the consideration of profit and loss leads to a qualitatively different optimal trading function. Our model additionally explains the diversity of CFMM designs that appear in practice. We show that careful analysis of our convex program enables inference of a market-maker beliefs about future asset prices, and show that these beliefs mirror the folklore intuition for several widely used CFMMs. Developing the program requires a new notion of the liquidity of a CFMM, and the core technical challenge is in the analysis of the KKT conditions of an optimization over an infinite-dimensional Banach space.

Bio: Mohak Goyal received the Bachelor of Technology and Master of Technology degrees in electrical engineering from the Indian Institute of Technology Bombay, Mumbai, India, in 2019. Since 2020, he has been working toward the Ph.D. degree with the Department of Management Science and Engineering, Stanford University, Stanford, CA, USA. From 2019 to 2020, he was an Engineer with Qualcomm Research India.
(In-person) October 18, 2023
Olga Klein (Warwick Business School)
Blockchain scaling and liquidity concentration on decentralized exchanges Link to paper
Abstract Liquidity providers (LPs) on decentralized exchanges (DEXs) can protect themselves from adverse selection risk by updating their positions more frequently. However, repositioning is costly, because LPs have to pay gas fees for each update. We analyze the causal relation between repositioning and liquidity concentration around the market price, using the entry of a blockchain scaling solution, Polygon, as our instrument. Polygon's lower gas fees allow LPs to update more frequently than on Ethereum. Our results demonstrate that higher repositioning intensity and precision lead to greater liquidity concentration, which benefits small trades by reducing their slippage.

Bio: Olga is an Assistant Professor of Finance and a research fellow at the Gillmore Center of Financial Technology at Warwick Business School. Olga's research interests are in the areas of market microstructure, algorithmic and high-frequency trading, liquidity, market efficiency and fintech. In particular, she studies the impact of technology on liquidity and efficiency of security prices, both on traditional as well as decentralized exchanges (DEX). In her recent research, she has been investigating how blockchain scaling solutions improve liquidity concentration on the largest DEX, Uniswap v3. Prior to joining WBS, she was a post-doctoral research fellow at E-Finance Lab of the University of Frankfurt. Olga holds a Ph.D. in Finance from the University of Mannheim, Germany. She received her MSc in Finance and Economics from the University of Magdeburg in Germany and her BSc in Economic Theory from the Kyiv-Mohyla Academy in Ukraine.
(In-person) October 25, 2023
Lorenzo Schoenleber (Collegio Carlo Alberto)
The Impermanent Loss In Yield Farming Link to paper
Abstract We propose a continuous-time stochastic model to analyze the dynamics of impermanent loss in liquidity pools in decentralized finance (DeFi) protocols. We replicate the impermanent loss using option portfolios for the individual tokens. To estimate the risk-neutral joint distribution of the tokens we minimize the Hansen–Jagannathan bound, which is useful for the valuation of options on relative prices and for calculating implied correlations. We then investigate the relationship between the impermanent loss, the implied quantities, and their risk premia in the cross-section of liquidity pools. We verify our theory using options traded on major centralized derivative exchanges.

Bio: Lorenzo is an Assistant Professor at the Collegio Carlo Alberto in Turin. His area of interest is asset pricing, especially within the area of option-implied information, asset management, and DeFi. He is associated with the Fintech & Digital Finance Chair at Paris Dauphine University. He obtained his Ph.D. in Finance at the Frankfurt School of Finance and Management in 2020. He earned his B.Sc. and M.Sc. at the University of Mannheim where he studied Business Mathematics.
June 14, 2023
Andreas Park (University of Toronto)
Learning from DeFi: Would Automated Market Makers Improve Equity Trading? Link to paper
Abstract We investigate the potential for automated market makers (AMMs) to be economically viable in and improve traditional financial markets. AMMs are a new type of trading institution that have emerged in the world of crypto-assets and process a significant portion of global crypto trading volume. The current trend of tokenizing assets, the legitimization of crypto-token issuance via the EU's MiCA regulation, and the push by the S.E.C. to change the trading of retail orders presents an opportunity to consider AMMs for traditional markets. Our approach is to determine the parameters that would allow liquidity providers to profitably contribute to an AMM and calculate, based on U.S. equity trading data, if liquidity demanders would benefit from using the AMM for these parameters. Our analysis suggests that properly designed AMMs could save U.S. investors about 30% of annual transaction costs. The source for these savings is twofold: AMMs allow better risk sharing for liquidity providers and they use locked-up capital that otherwise sits idly at brokerages. The introduction of AMMs in traditional markets could particularly improve the liquidity and trading cost issues faced by small firms, allowing them to attract more investors and capital.

Bio: Andreas Park is a Professor of Finance at the University of Toronto, appointed to the Rotman School of Management and the Department of Management at UTM. He currently serves as the Research Director at the FinHub, Rotman’s Financial Innovation Lab, he is the co-founder of LedgerHub, the University of Toronto’s blockchain research lab. He has served as a lab economist for the Blockchain stream at the Creative Destruction Lab. Andreas teaches courses on payments innovation, decentralized finance, and financial market trading, and his current research focuses on the economic impact of technological transformations such as blockchain technology. He recently co-authored a design proposal for a central-bank issued digital currency, commissioned by the Bank of Canada. Andreas received his doctorate from the University of Cambridge. His work has been published in top journals in economics and finance including Econometrica, the Journal of Finance, the Journal of Financial Economics, and the Journal of Financial and Quantitative Analysis."
May 31, 2023
Liyi Zhou (Imperial College)
We All Know That Audits Aren't Enough - Reshaping Blockchain Security Link to paper Link to second paper Link to third paper
Abstract While the DeFi ecosystem continues to grow, it remains vulnerable to a myriad of attacks and security threats. Traditional approaches, such as audits, have proven insufficient to fully secure the ecosystem. In this talk, Liyi Zhou will present a 0-to-1 paradigm shift to reshaping blockchain security. Zhou will introduce real-time Intrusion Detection and Prevention Systems (IDS/IPS) that are poised to revolutionize DeFi security. By addressing both the execution of DeFi attacks and the development of cutting-edge defensive mechanisms, Zhou aims to catalyze a new era of security and resilience within the DeFi ecosystem.

Bio: Liyi Zhou is a fourth-year Ph.D. candidate at Imperial College London, working under the guidance of Associate Professor Arthur Gervais. In close collaboration with fellow researcher Kaihua Qin, Zhou's research focuses on blockchain technology, decentralized finance, machine learning, and cybersecurity. Together, they have published numerous top-tier security conference papers, with Zhou contributing to over 15 papers in total during his Ph.D. journey. Driven by a passion for innovation, Zhou is committed go beyond incremental improvements in research to pioneering transformative 0-to-1 solutions and fostering collaboration between academia and practitioners.
May 17, 2023
Andrei Lyashenko (QRM, Illinois Institute of Technology)
Modeling Yield Curves with Factor HJM Link to paper
Abstract We introduce a novel risk-neutral interest rate modeling framework based on the factor modeling approach widely used to model yield curves in real-world applications. The new modeling framework combines the simplicity, intuitiveness, and computational efficiency of the factor modeling approach with the no-arbitrage rigor of pricing term structure models. Its constructive nature makes it a convenient practical tool for model development and brings clarity and intuition to the yield curve modeling process.

Bio: Andrei Lyashenko is the head of Market Risk and Pricing Models at the Quantitative Risk Management (QRM), Inc. in Chicago. His team is responsible for research, implementation and support of pricing and risk models across multiple asset classes. In November 2019, he was awarded the prestigious Quant of the Year award, jointly with Fabio Mercurio from Bloomberg, L.P., for their Risk Magazine paper on modeling backward-looking rates. Andrei is also adjunct professor at the Illinois Institute of Technology. Before joining the QRM in 1997, Andrei was on the mathematical faculty at the University of Illinois at Chicago and Iowa State University. Prior to coming to the US, he conducted academic research in applied math in Russia, Japan and Italy and published numerous research papers in the area of fluid stability in major mathematical journals. He holds a BSc in Mathematics from the Novosibirsk State University, Russia and a PhD in Mathematics from the Russian Academy of Science.
May 10, 2023
Rafael Nitchai (Universidade do Porto)
FPCS: Solving n-spends on a UTXO-based DLT Link to paper
Abstract The fast probabilistic consensus (FPC) is a leaderless voting consensus protocol that allows a set of nodes to agree on a value of a single bit. FPC is robust and efficient in Byzantine infrastructures and presents a low communicational complexity. In this paper, we introduce a modification of the Fast Probabilistic Consensus protocol (FPC) capable of achieving consensus on a maximal independent set of a graph —hence named Fast Probabilistic Consensus on a Set (FPCS)— that still preserves the robustness, effectiveness, and low communicational complexity of FPC. This paper shows that FPCS effectively resolves the problem (with high probability) of achieving consensus on a maximal independent set of a graph of conflicts (i.e. a maximal set of nonconflicting transactions) in the particular case of n-spend conflicts, even when a significant (but not major) proportion of nodes is malicious. These nodes intend to delay the consensus or even completely break it (meaning that nodes would arrive at different conclusions about the maximal independent set). Furthermore, the paper provides explicit estimates on the probability that the protocol finalizes in the consensus state in a given time. Our study refers to a specific implementation of cryptocurrencies, but the results hold for more general majority models.

Bio:
May 3, 2023
Claudio Tessone (University of Zurich)
From self-organisation to rug pulls in UniSwap Link to paper
Abstract UniSwap is the largest decentralised exchange (DEX) in terms of market capitalisation, and is widely recognised for introducing an Automated Market Maker (AMM) mechanism that provides liquidity and eliminates counterparty risk. However, UniSwap also poses several threats by itself due to its lack of regulation and operations scrutiny. Because of its decentralised nature, anyone can take two tokens with arbitrary supplies and pair them to form a liquidity pool (LP) on UniSwap; this LP allows the creator and other users to buy, sell or provide liquidity of any amount of tokens. These characteristics sometimes can lead to deceive and harm innocent users. In this research, we focus on extit{Rug-pull} attack and its effect on the liquidity of LPs and the whole Uniswap market, we detect Rug-pull events by retrieving and replaying each mint, swap, and burn event, and calculating the change ratio of the reserve of the primary tokens include WETH, USDT, USDC and DAI. Our results show that despite UniSwap being the largest and most popular DeFi platform, it still exhibits several anomalies in terms of liquidity, price, and attacks, including numerous LPs with extremely low total value locked (TVL) and tokens with extremely high or low prices, Rug-pull is a prevalent attack on Uniswap which not only directly causes many LP's price and liquidity anomalies but also has a significant impact on the stability and connectivity of the liquidity pool network. We also analyse the striking statistical regularities of the Liquidity network in UniSwap, a novel construct that allows to foresee the existence of simple mechanisms that drive the growth and sustainability of this decentralised marketplace.

Bio: Claudio J. Tessone is Professor of Blockchain and Distributed Ledger Technologies at the Informatics Department, University of Zurich. He is co-founder and Chairman of the UZH Blockchain Center. He holds a PhD in Physics (on complex systems) and an Habilitation on Complex socio-economic systems from ETH Zurich. He is an expert in the modelling of complex socio-economic, and socio-technical systems from an interdisciplinary perspective. He is interested in the link between microscopic agent behaviour and the rules these agents abide to, and the global, emergent properties of socio-economic and socio-technical systems. Blockchain-based systems and cryptocurrencies are the main pillar of his research (being among the first to study them). This includes crypoeconomics (from financial aspects to meso- and macro- properties, such as withstanding, emergent centralisation), big-data blockchain analytics and forensics, design of blockchain-based systems, and characterisation of economic incentives that are present (by design or set inadvertently) in them He is the director of the Summer School: Deep Dive into Blockchain and of the Certificate of Advanced Studies on Blockchain at the University of Zurich.
April 26, 2023
Bhaskar Krishnamachari (USC Viterbi School of Engineering)
Dynamic Curves: Enhancing Decentralized Autonomous Exchanges Link to paper Link to second paper Link to third paper
Abstract Cryptocurrency exchanges based on curve-based automated market makers have been a major development in decentralized finance (DeFi) because they enable efficient, secure, low-friction conversions between different cryptocurrencies. This research talk will explore the potential of dynamic AMM curves, optimal trading on such dynamic AMM curves, and the use of reinforcement learning to enhance AMMs. We will describe how dynamic curves enable autonomous exchanges to maintain a liquidity pool that continuously adjusts to the market price, and discuss how optimal trading policies can be derived for such a dynamic AMM. We will also discuss how a reinforcement learning agent can be used to optimize fees on automated market maker protocols.

Bio: Bhaskar Krishnamachari is a Professor of Electrical and Computer Engineering at the USC Viterbi School of Engineering. His research spans the design and evaluation of algorithms, protocols, and applications for wireless networks, distributed systems, and the internet of things. He is the co-author of more than 300 technical papers, and 3 books, that have been collectively cited more than 30,000 times. He has received best paper awards at IPSN (2004, 2010), Mobicom (2010), and VNC (2021). He is an IEEE Fellow.
April 19, 2023
Heimbach Lioba (ETH Zurich)
Turmoil in DeFi Lending Markets Link to paper
Abstract The merge marked the Ethereum blockchain's transition from proof-of-work (PoW) to proof-of-stake (PoS). However, ahead of the merge a fraction of the Ethereum ecosystem announced plans of continuing with a PoW chain. Owners of ETH - whether their ETH was borrowed or not - would hold the native tokens on each chain. This development alarmed lending protocols. They feared spiking ETH borrowing rates would lead to mass liquidations which could undermine their viability. Thus, the decentralized autonomous organization running the protocols saw no alternative to intervention - restricting users' ability to borrow. In November 2022, Avi Eisenberg performed an attack on AAVE. Eisenberg attempted to short the CRV token by using funds borrowed on the protocol to artificially deflate the value of CRV. While the attack was ultimately unsuccessful, it left the AAVE community scared and even raised question marks regarding the feasibility of large lending platforms under decentralized governance. Both events expose a predicament of DeFi lending protocols: limit the scope or compromise on 'decentralization'.

Bio: Distributed Computing Group at ETH.
March 8, 2023
Omer Suleman (Haruko)
Challenges in AMM Design and Implementation – A Platypus Case Study Link to paper Link to second paper
Abstract Automated Market Maker (AMM) platforms have become a core pillar within the cryptocurrency ecosystem, executing trades according to code and mathematical models that are publicly available and without the need for human intervention. The - code is law - premise has provided considerable economic benefits but has also produced new forms of market vulnerabilities through improperly implemented code or mathematical algorithms with unexpected behaviours. We present several such instances identified by Haruko during a Spring 2022 analysis of the code base and White/Yellow Papers of several prominent AMMs, with primary focus on the Platypus (http://platypus.finance) AMM developed on the Avalanche blockchain. Platypus uses -one sided liquidity-, a novel mathematical approach distinct from the more common -Constant Function- AMMs. We review this framework, including its fees, incentives, and anti-arbitrage penalties, before demonstrating that, despite such penalties, there exists an arbitrage vulnerability. We also identify, through numerical methods, the minimum swap fees required to block this arbitrage route – this result allowed the developers to address this vulnerability in the short term, until an update to platform's arbitrage protection can be developed.

Bio:
March 1, 2023
Deborah Miori (University of Oxford - Oxford-Man Institute)
DeFi: Data-Driven Characterisation of Uniswap v3 Ecosystem & an Ideal Crypto Law for Liquidity Pools Link to paper
Abstract Uniswap is a Constant Product Market Maker built around liquidity pools, where pairs of tokens are exchanged subject to a fee that is proportional to the size of transactions. At the time of writing, there exist more than 6,000 pools associated with Uniswap v3, implying that empirical investigations on the full ecosystem can easily become computationally expensive. Thus, we propose a systematic workflow to extract and analyse a meaningful but computationally tractable sub-universe of liquidity pools. Leveraging on the 34 pools found relevant for the six-months time window January-June 2022, we then investigate the related liquidity consumption behaviour of market participants. We propose to represent each liquidity taker by a suitably constructed transaction graph, which is a fully connected network where nodes are the liquidity taker’s executed transactions, and edges contain weights encoding the time elapsed between any two transactions. We extend the NLP-inspired graph2vec algorithm to the weighted undirected setting, and employ it to obtain an embedding of the set of graphs. This embedding allows us to extract seven clusters of liquidity takers, with equivalent behavioural patters and interpretable trading preferences. We conclude our work by testing for relationships between the characteristic mechanisms of each pool, i.e. liquidity provision, consumption, and price variation. We introduce a related ideal crypto law, inspired from the ideal gas law of thermodynamics, and demonstrate that pools adhering to this law are healthier trading venues in terms of sensitivity of liquidity and agents’ activity. Regulators and practitioners could benefit from our model by developing related pool health monitoring tools.

Bio: Deborah Miori is a Dphil candidate at University of Oxford.
February 22, 2023
Pierre-Olivier Goffard (ISFA, Lyon)
Stochastic models for blockchain analysis Link to paper
Abstract A blockchain is a distributed ledger maintained by achieving consensus in a P2P network. This talk focuses on the security of Proof-of-Work blockchains, more specifically on an attack called double spending. We first introduce some blockchain concepts along with a description of the Proof-of-Work protocol before setting up a mathematical model to compute the likelihood of a successful double spending attack.

Bio: http://pierre-olivier.goffard.me/
February 15, 2023
Andre Rzym (Man Group)
Crypto, is the Alpha worth the Pain? Link to paper
Abstract We describe our experience of, and observations on, the cryptocurrency space from the perspective of a regulated investment manager. We discuss the immaturity of the space, consider the impact of high volatility, and describe how the product development process is very different to other asset classes.

Bio: Partner and Portfolio Manager, Man AHL.
February 8, 2023
Philippe Bergault (Université Paris Dauphine)
Liquidity Providers in Automated Market Makers: a Mean-Variance Analysis of Payoffs Link to paper
Abstract We analyze the performance of Liquidity Providers (LPs) providing liquidity to different types of Automated Market Makers (AMMs). This analysis is carried out using a mean / standard deviation viewpoint à la Markowitz, though based on the PnL of LPs compared to that of agents holding coins outside of AMMs. We show that LPs tend to perform poorly in a wide variety of CFMMs under realistic market conditions. We then explore an alternative AMM design in which an oracle feeds the current market exchange rate to the AMM which then quotes a bid/ask spread. This allows us to define an efficient frontier for the performance of LPs in an idealized world with perfect information and to show that the smart use of oracles greatly improves LPs' risk / return profile, even in the case of a lagged oracle.

Bio: https://sites.google.com/view/bergaultphilippe
January 25, 2023
Marcello Monga (University of Oxford - Oxford-Man Institute)
Decentralised Finance and Automated Market Making: Execution and Speculation Link to paper
Abstract Automated market makers (AMMs) are a new prototype of trading venues which are revolutionising the way market participants interact. At present, the majority of AMMs are constant function market makers (CFMMs) where a deterministic trading function determines how markets are cleared. A distinctive characteristic of CFMMs is that execution costs are given by a closed-form function of price, liquidity, and transaction size. This gives rise to a new class of trading problems. We focus on constant product market makers and show how to optimally trade a large position in an asset and how to execute statistical arbitrages based on market signals. We employ stochastic optimal control tools to devise two strategies. One strategy is based on the dynamics of prices in competing venues and assumes constant liquidity in the AMM. The other strategy assumes that AMM prices are efficient and liquidity is stochastic. We use Uniswap v3 data to study price, liquidity, and trading cost dynamics, and to motivate the models. Finally, we perform consecutive runs of in-sample estimation of model parameters and out-of-sample liquidation and arbitrage strategies to showcase the performance of the strategies.

Bio: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4144743
January 18, 2023
Agostino Capponi (Columbia University)
The Information Content of Blockchain Fees Link to paper
Abstract Trading at decentralized exchanges (DEXs) requires traders to bid blockchain fees to determine the execution priority of their orders. We employ a structural vector-autoregressive (structural VAR) model to provide evidence that DEX trades with high fees not only reveal more private information, but also respond more to public price innovations on centralized exchanges (CEXs), contributing to price discovery. Using a unique dataset of Ethereum mempool orders, we further demonstrate that high fees do not result from traders competing with each other on private or public information. Rather, our analysis lends support to the hypothesis that they bid high fees to reduce the execution risk of their orders due to blockchain congestion.

Bio: http://www.columbia.edu/~ac3827/
December 21, 2022
Jack Chong (University of Oxford, frigg.eco)
An Unreal Primer on Real World Assets (RWAs)
Abstract An Unreal Primer on Real World Assets (RWAs)

Bio: https://www.linkedin.com/in/jack-chong/
December 14, 2022
Kristof Lommers (University of Oxford, Saïd Business School)
Market Making in NFTs Link to paper
Abstract This study discusses a framework for market making in Non-Fungible Tokens (NFTs) which represent unique digital assets in a low liquidity and high price volatility environment. The market making problem differs from fungible cryptocurrencies as there is no layered orderbook structure of market depth and market makers would need to hold inventory on the other side of the trades for a non-negligible horizon. We have developed a model for prices in market making context in terms of embedded optionality of trading an NFT at either the floor or a price that is closer to the appraisal value. In order to develop the model for optionality of trading an NFT, we have defined a model on the joint price dynamics of the NFT and its corresponding floor. The price dynamics were decomposed into an intrinsic price diffusion process and jump components relating to liquidity events. Besides NFTs, the approach presented in this paper could provide insights for market making in other ”non- fungible” asset classes such as art or housing.

Bio: https://www.linkedin.com/in/kristoflommers
December 7, 2022
Francisco Marmolejo Cossio (Harvard University)
Differential Liquidity Provision in Uniswap V3 and Implications for Contract Design Link to paper
Abstract Decentralized exchanges (DEXs) facilitate trading assets on-chain without the need of a trusted third party. Amongst these, constant function market maker DEXs such as Uniswap handle the most volume of trades between ERC-20 tokens. In Uniswap v3, liquidity providers (LPs) are given the option to differentially allocate liquidity to be used for trades that occur within specific price intervals. We formalize the profit and loss that LPs can earn in simplified trade dynamics and are able to compute optimal liquidity allocations for liquidity providers who hold fixed price trajectory beliefs. We use this tool to shed light on the design question regarding how v3 contracts should partition price space for permissible liquidity allocations. Our results suggest that a richer space of potential partitions can simultaneously benefit both LPs and traders.

Bio: https://www.fmarmolejo.com/
November 30, 2022
Ronnie Sircar (Princeton University)
Cryptocurrencies, Mining & Mean Field Games Link to paper
Abstract We present a mean field game model to study the question of how centralization of reward and computational power occur in Bitcoin-like cryptocurrencies. Miners compete against each other for mining rewards by increasing their computational power. This leads to a novel mean field game of jump intensity control, which we solve explicitly for miners maximizing exponential utility, and handle numerically in the case of miners with power utilities. We show that the heterogeneity of their initial wealth distribution leads to greater imbalance of the reward distribution, or a ``rich get richer'' effect. This concentration phenomenon is aggravated by a higher bitcoin mining reward, and reduced by competition. Additionally, an advantaged miner with cost advantages such as access to cheaper electricity, contributes a significant amount of computational power in equilibrium, unaffected by competition from less efficient miners. Hence, cost efficiency can also result in the type of centralization seen among miners of cryptocurrencies.

Bio: RONNIE SIRCAR is the Eugene Higgins Professor of Operations Research and Financial Engineering (ORFE) at Princeton University, and is affiliated with the Bendheim Center for Finance, the Program in Applied and Computational Mathematics, and the Andlinger Center for Energy and the Environment. He received his doctorate from Stanford University, and taught for three years at the University of Michigan in the Department of Mathematics. He has received continuing National Science Foundation research grants since 1998. He was a recipient of the E-Council Excellence in Teaching Award for his teaching in 2002, 2005 and 2006, and the Howard B. Wentz Jr. Junior Faculty Award in 2003. His research interests center on Financial Mathematics, stochastic volatility models, energy markets and exhaustible resources, credit risk, asymptotic and computational methods, portfolio optimization and stochastic control problems, and stochastic differential games. He is a co-author of the book 'Multiscale Stochastic Volatility for Equity, Interest-Rate and Credit Derivatives', published by Cambridge University Press in 2011, and was founding co-editor-in-chief of the SIAM Journal on Financial Mathematics, from 2009-2015. He was Director of Graduate Studies for the Master in Finance program at the Bendheim Center for Finance from 2015-2018. He is the current Chair of the ORFE department. He was made a Fellow of the Society for Industrial and Applied Mathematics (SIAM) in 2020 for 'contributions to financial mathematics and asymptotic methods for stochastic control and differential games.'
November 23, 2022
Fayçal Drissi (University of Oxford - Oxford-Man Institute)
Decentralised Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision Link to paper
Abstract We introduce a new comprehensive metric of predictable loss (PL) for liquidity providers in constant function automated market makers and derive an optimal liquidity provision strategy. PL compares the value of the LP's holdings in the liquidity pool (assuming no fee revenue) with that of a self-financing portfolio that replicates the LP's holdings and invests in a risk-free account. We provide closed-form formulae for PL, and show that the losses stem from two sources: the convexity cost, which depends on liquidity taking activity and the convexity of the pool's trading function; the opportunity cost, which is due to locking the LP's assets in the pool. For LPs in constant product market makers with concentrated liquidity, we derive a closed-form strategy that dynamically adjusts the range around the exchange rate as a function of market trend, volatility, and liquidity taking activity in the pool. We prove that the profitability of liquidity provision depends on the tradeoff between PL and fee income. Finally, we use Uniswap v3 data to show that LPs have traded at a significant loss, and to show that the out-of-sample performance of our strategy is considerably superior to the historical performance of LPs in the pool we consider.

Bio: Fayçal Drissi is a PhD candidate at Université Paris 1 Panthéon-Sorbonne.
November 16, 2022
Deborah Miori (University of Oxford - Oxford-Man Institute)
An overview of Uniswap
Abstract An overview of the main features and innovations described in Uniswap v1, v2 and v3 whitepapers
November 9, 2022
Deborah Miori (University of Oxford - Oxford-Man Institute)
A review of essential principles of decentralized finance

About DeFOx

Organisers: Álvaro Cartea, Mihai Cucuringu, Fayçal Drissi, Deborah Miori, Marcello Monga

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