Related papers: Chasing price drains liquidity
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…
This paper mathematically models a constant-function automated market maker (CFAMM) position as a portfolio of exotic options, known as perpetual American continuous-installment (CI) options. This model replicates an AMM position's delta at…
Liquidity and trading activity on constant function market makers (CFMMs) such as Uniswap, Curve, and Balancer has grown significantly in the second half of 2020. Much of the growth of these protocols has been driven by incentivized pools…
We construct liquidity-adjusted return and volatility using purposely designed liquidity metrics (liquidity jump and liquidity diffusion) that incorporate additional liquidity information. Based on these measures, we introduce a…
With the emergence of decentralized finance, new trading mechanisms called Automated Market Makers have appeared. The most popular Automated Market Makers are Constant Function Market Makers. They have been studied both theoretically and…
Constant-function market makers (CFMMs), such as Uniswap, are automated exchanges offering trades among a set of assets. We study their technical relationship to another class of automated market makers, cost-function prediction markets. We…
We propose a simple non-equilibrium model of a financial market as an open system with a possible exchange of money with an outside world and market frictions (trade impacts) incorporated into asset price dynamics via a feedback mechanism.…
We consider a retailer selling a single product with limited on-hand inventory over a finite selling season. Customer demand arrives according to a Poisson process, the rate of which is influenced by a single action taken by the retailer…
The Generalized fractional Brownian motion (gfBm) is a stochastic process that acts as a generalization for both fractional, sub-fractional, and standard Brownian motion. Here we study its use as the main driver for price fluctuations,…
In this paper we analyze constant product market makers (CPMMs). We formalize the liquidity providers' profitability conditions and introduce a concept we call the profitability frontier in the xyk-space. We study the effect of mint and…
In this paper, we introduce a novel pricing model for Uniswap V3, built upon stochastic processes and the Martingale Stopping Theorem. This model innovatively frames the valuation of positions within Uniswap V3. We further conduct a…
Liquidity providers (LPs) are essential figures in the operation of automated market makers (AMMs); in exchange for transaction fees, LPs lend the liquidity that allows AMMs to operate. While many prior works have studied the incentive…
In this paper, we will consider a governance token pricing algorithm that conducts liquidity operations on AMM (CPMM) DEXs (automated market maker decentralized exchanges) with liquidity that belongs to a decentralized autonomous…
A novel high-frequency market-making approach in discrete time is proposed that admits closed-form solutions. By taking advantage of demand functions that are linear in the quoted bid and ask spreads with random coefficients, we model the…
We consider a dynamic pricing problem under unknown demand models. In this problem a seller offers prices to a stream of customers and observes either success or failure in each sale attempt. The underlying demand model is unknown to the…
In this paper, we propose a minimal model beyond geometric Brownian motion that aims to describe price actions with market inefficiency. From simple financial theory considerations, we arrive at a simple two-variable hidden Markovian time…
Two popular forms of automated market makers are constant sum and constant product (CSMM and CPMM respectively). Each has its advantages and disadvantages: CSMMs have stable exchange rates but are vulnerable to arbitrage and can sometimes…
We introduce a dynamic model in which a developer incrementally improves a product of uncertain quality over time, with the quality evolving as a controlled Brownian motion. At each moment in time, the developer can continue exploring by…
We consider the market microstructure of automated market makers (AMMs) from the perspective of liquidity providers (LPs). Our central contribution is a ``Black-Scholes formula for AMMs''. We identify the main adverse selection cost…
We introduce a new class of automated market maker (AMM), the \emph{partially active automated market maker} (PA-AMM). PA-AMM divides its reserves into two parts, the active and the passive parts, and uses only the active part for trading.…