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This article analytically characterizes the impermanent loss for automatic market makers in decentralized exchanges such as Uniswap or Balancer (CPMM). We present a theoretical static replication formula for the pool value using a…
This paper presents a discrete-time option pricing model that is rooted in Reinforcement Learning (RL), and more specifically in the famous Q-Learning method of RL. We construct a risk-adjusted Markov Decision Process for a discrete-time…
Decentralized Finance (DeFi) has revolutionized financial markets by enabling complex asset-exchange protocols without trusted intermediaries. Automated Market Makers (AMMs) are a central component of DeFi, providing the core functionality…
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…
The study proposes a quote-driven predictive automated market maker (AMM) platform with on-chain custody and settlement functions, alongside off-chain predictive reinforcement learning capabilities to improve liquidity provision of…
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…
Decentralized finance (DeFi) applications depend on accurate price oracles to ensure secure transactions, yet these oracles are highly vulnerable to manipulation, enabling attackers to exploit smart contract vulnerabilities for unfair asset…
Automated Market Makers (AMMs) are a cornerstone of decentralized finance. They are smart contracts (stateful programs) running on blockchains. They enable virtual token exchange: traders swap tokens with the AMM for a fee, while liquidity…
In a universal framework that expresses any market system in terms of state transition rules, we prove that every DeFi market system has an invariant function and is thus by definition a CFMM; indeed, all automated market makers (AMMs) are…
Within this work we consider an axiomatic framework for Automated Market Makers (AMMs). AMMs are smart contracts that set prices for swaps on a pool of assets. By imposing reasonable axioms on the underlying utility function, we are able to…
We investigate the market microstructure of Automated Market Makers (AMMs), the most prominent type of blockchain-based decentralized exchanges. We show that the order execution mechanism yields token value loss for liquidity providers if…
A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for…
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's…
In decentralized finance (DeFi), designing fixed-income lending automated market makers (AMMs) is extremely challenging due to time-related complexities. Moreover, existing protocols only support single-maturity lending. Building upon the…
Blockchains have popularized automated market makers (AMMs). An AMM exchange is an application running on a blockchain which maintains a pool of crypto-assets and automatically trades assets with users governed by some pricing function that…
Batch auctions are a classical market microstructure, acclaimed for their fairness properties, and have received renewed interest in the context of blockchain-based financial systems. Constant function market makers (CFMMs) are another…
In Decentralized Finance (DeFi), automated market makers typically implement liquidity provisioning protocols. These protocols allow third-party liquidity providers (LPs) to provide assets to facilitate trade in exchange for fees. This…
We consider a model of linear market impact, and address the problem of replicating a contingent claim in this framework. We derive a non-linear Black-Scholes Equation that provides an exact replication strategy. This equation is fully…
To reduce complexity and achieve scalable performance in high-dimensional black-box settings, we propose a distributed method for nonconvex derivative-free optimization of continuous variables with an additively separable objective, subject…
Recently emerging Decentralized Finance (DeFi) takes the promise of cryptocurrencies a step further, leveraging their decentralized networks to transform traditional financial products into trustless and transparent protocols that run…