Jason Milionis, Ciamac C. Moallemi, Tim Roughgarden
We consider the impact of trading fees on the profits of arbitrageurs trading against an automated market maker (AMM) or, equivalently, on the adverse selection incurred by liquidity providers (LPs) due to arbitrage. We extend the model of Milionis et al. [2022] for a general class of two asset AMMs to introduce both fees and discrete Poisson block generation times. In our setting, we are able to compute the expected instantaneous rate of arbitrage profit in closed form. When the fees are low, in the fast block asymptotic regime, the impact of fees takes a particularly simple form: fees simply scale down arbitrage profits by the fraction of blocks which present profitable trading opportunities to arbitrageurs. This fraction decreases with an increasing block rate, hence our model yields an important practical insight: faster blockchains will result in reduced LP losses. Further introducing gas fees (fixed costs) in our model, we show that, in the fast block asymptotic regime, lower gas fees lead to smaller losses for LPs.
By investigating nonfungible tokens (NFTs), we provide the first systematic study of retail investor behavior through asset bubbles. Given that NFTs are recorded in public blockchains, we are able to track investor behavior over time, leading to the identification of numerous price run-ups and crashes. Our study reveals that agent-level variables, such as investor sophistication, heterogeneity, and wash trading, in addition to aggregate variables, such as volatility, price acceleration, and turnover, significantly predict bubble formation and price crashes. We find that sophisticated investors consistently outperform others and exhibit characteristics consistent with superior information and skills, supporting the narrative surrounding asset pricing bubbles.
Liquidations in Decentralized Finance (DeFi) are both a blessing and a curse -- whereas liquidations prevent lenders from capital loss, they simultaneously lead to liquidation spirals and system-wide failures. Since most lending and borrowing protocols assume liquidations are indispensable, there is an increased interest in alternative constructions that prevent immediate systemic-failure under uncertain circumstances. In this work, we introduce reversible call options, a novel financial primitive that enables the seller of a call option to terminate it before maturity. We apply reversible call options to lending in DeFi and devise Miqado, a protocol for lending platforms to replace the liquidation mechanisms. To the best of our knowledge, Miqado is the first protocol that actively mitigates liquidations to reduce the risk of liquidation spirals. Instead of selling collateral, Miqado incentivizes external entities, so-called supporters, to top-up a borrowing position and grant the borrower additional time to rescue the debt. Our simulation shows that Miqado reduces the amount of liquidated collateral by 89.82% in a worst-case scenario.
This paper examines the response of major cryptocurrencies to macroeconomic news announcements (MNA). While other cryptocurrencies exhibit no reaction to major MNA, Bitcoin responds negatively to inflation surprise. Price of Bitcoin decreases by 24 bps in response to a 1 standard deviation inflationary surprise. This reaction is inconsistent with widely-held beliefs of practitioners that Bitcoin can hedge inflation. I do not find support for the hypothesis that the negative response of Bitcoin to inflation is due to its negative exposure to interest rates. Instead, I find support for the hypothesis that Bitcoin is strongly affected by the shift in consumption-savings decisions, driven by the rise in inflation. Consistent with this view, Bitcoin has negative exposure to a proxy for the consumption-savings ratio.
Songrun He, Asaf Manela, Omri Ross, Victor von Wachter
Perpetual futures are the most popular cryptocurrency derivatives. Perpetuals offer leveraged exposure to their underlying without rollover or direct ownership. Unlike fixed-maturity futures, perpetuals are not guaranteed to converge to the spot price. To minimize the gap between perpetual and spot prices, long investors periodically pay shorts a funding rate proportional to this difference. We derive no-arbitrage prices for perpetual futures in frictionless markets and bounds in markets with trading costs. Empirically, deviations from these prices in crypto are larger than in traditional currency markets, comove across currencies, and diminish over time. An implied arbitrage strategy yields high Sharpe ratios.
Abrar Rahman, Victor Shi, Matthew Ding, Elliot H. Choi
Synthetic assets are decentralized finance (DeFi) analogues of derivatives in the traditional finance (TradFi) world - financial arrangements which derive value from and are directly pegged to fluctuations in the value of an underlying asset (ex: futures and options). Synthetic assets occupy a unique niche, serving to facilitate currency exchange, giving traders a means to speculate on the value of crypto assets without directly holding them, and powering more complex financial tools such as yield optimizers and portfolio management suites. Unfortunately, the academic literature on this topic is highly disparate and struggles to keep up with rapid changes in the space. We present the first Systematization of Knowledge (SoK) in this area, focusing on presenting the key mechanisms, protocols, and issues in an accessible fashion to highlight risks for participants as well as areas of research interest. This paper takes a broad perspective in establishing a general framework for synthetic assets, from the ideological origins of crypto to legal barriers for firms in this space, encapsulating the basic mechanisms underpinning derivatives markets as well as presenting data-driven analyses of major protocols.
Lioba Heimbach, Eric Schertenleib, Roger Wattenhofer
Financial markets have evolved over centuries, and exchanges have converged to rely on the order book mechanism for market making. Latency on the blockchain, however, has prevented decentralized exchanges (DEXes) from utilizing the order book mechanism and instead gave rise to the development of market designs that are better suited to a blockchain. Although the first widely popularized DEX, Uniswap V2, stood out through its astonishing simplicity, a recent design overhaul introduced with Uniswap V3 has introduced increasing levels of complexity aiming to increase capital efficiency. In this work, we empirically study the ability of Unsiwap V3 to handle unexpected price shocks. Our analysis finds that the prices on Uniswap V3 were inaccurate during the recent abrupt price drops of two stablecoins: UST and USDT. We identify the lack of agility required of Unsiwap V3 liquidity providers as the root cause of these worrying price inaccuracies. Additionally, we outline that there are too few incentives for liquidity providers to enter liquidity pools, given the elevated volatility in such market conditions.
Mnacho Echenim, Emmanuel Gobet, Anne-Claire Maurice
We design a novel calibration procedure that is designed to handle the specific characteristics of options on cryptocurrency markets, namely large bid-ask spreads and the possibility of missing or incoherent prices in the considered data sets. We show that this calibration procedure is significantly more robust and accurate than the standard one based on trade and mid-prices.
Tether Limited has the sole authority to create (mint) and destroy (burn) Tether stablecoins (USDT). This paper investigates Bitcoin's response to USDT supply change events between 2014 and 2021 and identifies an interesting asymmetry between Bitcoin's responses to USDT minting and burning events. Bitcoin responds positively to USDT minting events over 5- to 30-minute event windows, but this response begins declining after 60 minutes. State-dependence is also demonstrated, with Bitcoin prices exhibiting a greater increase when the corresponding USDT minting event coincides with positive investor sentiment and is announced to the public by data service provider, Whale Alert, on Twitter.
The current design space of derivatives in Decentralized Finance (DeFi) relies heavily on oracle systems. Replicating market makers (RMMs) provide a mechanism for converting specific payoff functions to an associated Constant Function Market Makers (CFMMs). We leverage RMMs to replicate the approximate payoff of a Black-Scholes covered call option. RMM-01 is the first implementation of an on-chain expiring option mechanism that relies on arbitrage rather than an external oracle for price. We provide frameworks for derivative instruments and structured products achievable on-chain without relying on oracles. We construct long and binary options and briefly discuss perpetual covered call strategies commonly referred to as "theta vaults." Moreover, we introduce a procedure to eliminate liquidation risk in lending markets. The results suggest that CFMMs are essential for structured product design with minimized trust dependencies.
Panoptic is the perpetual, oracle-free, instant-settlement options trading protocol on the Ethereum blockchain. Panoptic enables the permissionless trading of options on top of any asset pool in the Uniswap v3 ecosystem and seeks to develop a trustless, permissionless, and composable options product, i.e., do for decentralized options markets what x*y=k automated market maker protocols did for spot trading.
On September 15, 2022, the Ethereum network adopted a proof-of-stake (PoS) consensus mechanism. We study the impact on the network and competing platforms in a two month event window around the Beacon chain merge. We find that the transition to PoS has reduced energy consumption by 99.98%. Miners have not transformed into validators, and total block reward income (in USD) has fallen by 97%, though transaction fees (in ETH) for Ether have increased nearly 10%. The Herfindahl index for the top 10 is 1,009; the network is 19% less concentrated after the merge. Ethereum supply growth has been deflationary since the merge. The time between consecutive blocks is now steady at 12 seconds and transactions per day are up 7.0%. On Polygon, Matic fees rose but token fees fell. Polygon also slows, processing 3.3% fewer transactions per day. Solana's fees fall by $0.0003, and transactions per day are down 48%. Stablecoin transfer volumes fall on Ethereum and Polygon, but rise on Solana.
This research proposes a model for the intraday variation between the ETHBTC spot and the quotient of ETHUSDT and BTCUSDT traded on Binance. Under conditions of no-arbitrage, perfect accuracy and no microstructure effects, the variation must be equal to its theoretically computed value of 0. We conduct our research on 4 years of data. We find that the variation is not constantly 0. The variation shows a fluctuating behaviour on either side of 0. Furthermore, the deviations tend to be larger in the first year than the rest of the years. We test the sample for the nature of diffusion where we find evidence of mean-reversion. We model the variation using an Ornstein-Uhlenbeck process. A maximum likelihood estimation procedure is used. From the accuracy of the sampling distribution of the parameters obtained, we conclude that the variation may be accurately modelled as an Ornstein-Uhlenbeck process. From the parameters obtained, the long-term mean is shown to have a negative sign and differs from the theoretical value of 0 at 1e-05 precision. We take note of the results in light of efficiency of the markets to price publicly known information.
We study recurrent patterns in volatility and volume for major cryptocurrencies, Bitcoin and Ether, using data from two centralized exchanges (Coinbase Pro and Binance) and a decentralized exchange (Uniswap V2). We find systematic patterns in both volatility and volume across day-of-the-week, hour-of-the-day, and within the hour. These patterns have grown stronger over the years and can be related to algorithmic trading and funding times in futures markets. We also document that price formation mainly takes place on the centralized exchanges while price adjustments on the decentralized exchanges can be sluggish.
We review different classes of cryptocurrencies with emphasis on their economic properties. Pure-asset coins such as Bitcoin, Ethereum and Ripple are characterized by not being a liability of any economic agent and most resemble commodities such as gold. Central bank digital currencies, at the other end of the economic spectrum, are liabilities of a Central Bank and most resemble cash. In between, there exist a range of so-called stable coins, with varying degrees of economic complexity. We use balance sheet operations to highlight the properties of each class of cryptocurrency and their potential uses. In addition, we propose the basic structure for a macroeconomic model incorporating all the different types of cryptocurrencies under consideration.
In this paper, we study a pricing problem of the multiple reset put option, which allows the holder to reset several times a current strike price to obtain an at-the-money European put option. We formulate the pricing problem as a multiple optimal stopping problem, then reduce it to a sequence of single optimal stopping problems and study the associated free-boundary problems. We solve this sequence of problems by induction in the number of remaining reset rights and exploit probabilistic arguments such as local time-space calculus on curves. As a result, we characterize each optimal reset boundary as the unique solution to a nonlinear integral equation and derive the reset premium representations for the option prices. We propose that the multiple reset options can be used as cryptocurrency derivatives and an attractive alternative to standard European options due to the extreme volatility of underlying cryptocurrencies.
This study examines the dynamic asset market linkages under the COVID-19 global pandemic based on market efficiency, in the sense of Fama (1970). Particularly, we estimate the joint degree of market efficiency by applying Ito et al.'s (2014; 2017) Generalized Least Squares-based time-varying vector autoregression model. The empirical results show that (1) the joint degree of market efficiency changes widely over time, as shown in Lo's (2004) adaptive market hypothesis, (2) the COVID-19 pandemic may eliminate arbitrage and improve market efficiency through enhanced linkages between the asset markets; and (3) the market efficiency has continued to decline due to the Bitcoin bubble that emerged at the end of 2020.
Unihedge is a decentralized platform for prediction markets with a novel approach. Using Harberger Tax (HTAX) economic policies a new type of prediction market, named HTAX prediction market, was build. HTAX prediction market derivates from Dynamic PariMutuel (DPM) type of prediction markets thus offering its users an unlimited liquidity for any preferred time horizon. It tries to solve some problems of DPM by introducing a new incentive mechanism to support early information incorporation and a protection against share readjustment for hedgers. In the paper also implementation of platform on Ethereum Virtual Machine (EVM) is presented with the usage of Decentralized Exchange (DEX) as an price discovery mechanism for prediction market resolutions.
Over 90% of exchange trading on crypto options has always been on the Deribit platform. This centralised crypto exchange only lists inverse products because they do not accept fiat currency. Currently, fiat-based traders can only make deposits in bitcoin, although they can withdraw both bitcoin and ether to their on-chain wallets. Likewise, other major crypto options platforms only list crypto--stablecoin trading pairs in so-called direct options, which are similar to the standard crypto options listed by the CME except the U.S. dollar is replaced by a stablecoin version. Until now a clear mathematical exposition of these products has been lacking. We discuss the sources of market incompleteness in direct and inverse options and compare their pricing and hedging characteristics. Then we discuss the useful applications of currency protected "quanto" direct and inverse options for fiat-based traders and describe their pricing and hedging characteristics, all in the Black-Scholes setting.
A model is proposed for Bitcoin prices that takes into account market attention. Market attention, modeled by a mean-reverting Cox-Ingersoll-Ross processes, affects the volatility of Bitcoin returns, with some delay. The model is affine and tractable, with closed formulae for the conditional characteristic functions with respect to both the conventional and a delayed filtration. This leads to semi-closed formulae for European call and put prices. A maximum likelihood estimation procedure is provided, as well as a method for changing to a risk-neutral measure. The model compares very well against classical and attention-based models when tested on real data.
We study to what extent the Bitcoin blockchain security permanently depends on the underlying distribution of cryptocurrency market outcomes. We use daily blockchain and Bitcoin data for 2014-2019 and employ the ARDL approach. We test three equilibrium hypotheses: (i) sensitivity of the Bitcoin blockchain to mining reward; (ii) security outcomes of the Bitcoin blockchain and the proof-of-work cost; and (iii) the speed of adjustment of the Bitcoin blockchain security to deviations from the equilibrium path. Our results suggest that the Bitcoin price and mining rewards are intrinsically linked to Bitcoin security outcomes. The Bitcoin blockchain security's dependency on mining costs is geographically differenced - it is more significant for the global mining leader China than for other world regions. After input or output price shocks, the Bitcoin blockchain security reverts to its equilibrium security level.
Peter P. Rohde, Vijay Mohan, Sinclair Davidson, Chris Berg · 7 authors
Two of the most important technological advancements currently underway are the advent of quantum technologies, and the transitioning of global financial systems towards cryptographic assets, notably blockchain-based cryptocurrencies and smart contracts. There is, however, an important interplay between the two, given that, in due course, quantum technology will have the ability to directly compromise the cryptographic foundations of blockchain. We explore this complex interplay by building financial models for quantum failure in various scenarios, including pricing quantum risk premiums. We call this quantum crypto-economics.
We present positive evidence of price stability of cryptocurrencies as a medium of exchange. For the sample years from 2016 to 2020, the prices of major cryptocurrencies are found to be stable, relative to major financial assets. Specifically, after filtering out the less-than-one-month cycles, we investigate the daily returns in US dollars of the major cryptocurrencies (i.e., Bitcoin, Ethereum, and Ripple) as well as their comparators (i.e., major legal tenders, the Euro and Japanese yen, and the major stock indexes, S&P 500 and MSCI World Index). We examine the stability of the filtered daily returns using three different measures. First, the Pearson correlations increased in later years in our sample. Second, based on the dynamic time-warping method that allows lags and leads in relations, the similarities in the daily returns of cryptocurrencies with their comparators have been present even since 2016. Third, we check whether the cumulative sum of errors to predict cryptocurrency prices, assuming stable relations with comparators' daily returns, does not exceeds the bounds implied by the Black-Scholes model. This test, in other words, does not reject the efficient market hypothesis.
The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study the hedge behaviour and effectiveness for the class of affine jump diffusion models and infinite activity Levy processes. First, market data is calibrated to stochastic volatility inspired (SVI)-implied volatility surfaces to price options. To cover a wide range of market dynamics, we generate Monte Carlo price paths using an SVCJ model (stochastic volatility with correlated jumps), a close-to-actual-market GARCH-filtered kernel density estimation as well as a historical backtest. In all three settings, options are dynamically hedged with Delta, Delta-Gamma, Delta-Vega and Minimum Variance strategies. Including a wide range of market models allows to understand the trade-off in the hedge performance between complete, but overly parsimonious models, and more complex, but incomplete models. The calibration results reveal a strong indication for stochastic volatility, low jump frequency and evidence of infinite activity. Short-dated options are less sensitive to volatility or Gamma hedges. For longer-dated options, tail risk is consistently reduced by multiple-instrument hedges, in particular by employing complete market models with stochastic volatility.