Coexisting Exchange Platforms: Limit Order
Books and Automated Market Makers 

Jun Aoyagi & Yuki Ito

Discussion by Katya Malinova

DeGroote School of Business

McMaster University

CBER Conference

May 2022, Boston

Decentralized Exchanges: Why Important?

  • Blockchain: infrastructure for value exchange
    • \(\to \)  trading?!
    • But infrastructure \(\ne\) market
  • How do you organize a marketplace on-chain?
    • Limit order book?
      • Very challenging
        • monitor & re-quote \(\to\)  gas fees to change orders, all nodes have to update, ...
    • Centralized market \(\to\) off-chain, missing out on the infrastructure
  • Decentralized exchanges & AMM!!
    • Pool liquidity, automate pricing
    • HUGE!

A genuinely novel market institution: how does it interact with the existing ones?

Multiple markets & their co-existence

  • A long-standing issue in finance
  • Different markets/pricing structures co-exist in practice
  • Yet, theoretically, co-existence is less obvious
    • Pagano (1989, QJE) "Trading Volume and Asset Liquidity"
      • co-existence is either a knife-edge, or heavily relies on trader conjectures
      • "clustering" by size
    • Glosten (1994, JF) "Is the Electronic Open Limit Order Book Inevitable?"
    • Back & Baruch (2007, JF) "Working orders in limit order markets and floor exchanges"
      • "Equivalent" equilibria under the two different pricing structures
    • Zhu (2014, RFS) "“Do dark pools harm price discovery?"
      • Informed concentrate on lit exchanges (and only trade on lit for low volatility)

Co-existence of DEX & CEX: very exciting topic!

  • Traditionally: 
    • different markets = markets with different pricing structures
  • DEX vs. CEX
    • different pricing structures
    • different custody arrangements
      • possibly different use value to trading/holding a token on DEX vs CEX
    • different settlement arrangements & a whole new set of players (validators)
      • possible attacks on pending transactions 
      • \(\to\) next paper in this session!

Several papers on AMM 

  • Capponi and Jia (2021)
    • welfare of the liquidity providers on the DEX
    • conditions for the liquidity breakdowns
  • Lehar & Parlour (2021)
    • compare the two markets "in isolation" + empirics on UniSwap
    • when is the DEX superior?
  • Park (2021)
    • compares different pricing functions & the desired properties
    • do (and which) pricing functions give rise to attacks on pending transactions & MEV?
  • This paper: 
    • examine co-existence of DEX and CEX
  • Focus on the novel pricing on DEX
  • Search for an equilibrium where a DEX co-exists with a limit order book
    • \(\to\) it exists and stable
  • Empirical predictions
    • Buy vs. sell asymmetry of the price impact on DEX
      • \(\to\) informed buyers vs sellers differ in DEX vs CEX preferences \(\to\) asymmetry in buy vs sell order info 
    • Complementarities in DEX & CEX liquidity

This paper

 

  • Relate the results to existing theoretical literature on co-existence 
    • Are the issues identified in existing literature surface here?
    • And if not, what is key to robust co-existence here?

General Comments & Questions

  • Are there equilibria where trading concentrates on a single market?  
  • Focus on a particular parameter for an interior solution
    • How large is this parameter region?
  • Are the pricing diffs + info the main ingredients to understand DEX vs. CEX?
    • The role of other differences? 
  • Model-wise, the limit order book on CEX is very stylized: how critical is it?
  • Price discovery?

 

  • Period 1: Liquidity providers ("market makers")
    • post quotes on CEX & provide liquidity on DEX 
  • Period 2:
    • Change in the fundamental \(\to\) Informed liquidity demanders
      • All trade in the same direction 
      • Continuum of them \(\to\) trading fully reveals the info
    • No change in the fundamental \(\to\) "Noise" liquidity demanders
      • A continuum of them
      • Buy demand = sell demand \(\to\) no imbalance
  • Period 3 (if there was a change in the fundamental):
    • Arbitrageurs on DEX
    • Liquidity providers re-quote on CEX

Model Recap: Who and When?

Model Recap: Where & How?

DEX

  • "Limit order book"
    • but not discriminatory
  • Liquidity demanders enter sequentially but:
    • all pay the same ask
    • \(\to\) no price impact cost from "earlier"/faster entrants on later ones
    • no "walking the book", no MM re-quoting
  • Costs:
    • informed & noise pay the same bid-ask spread 

CEX

  • Bonding curve \(\to\)  price
    • "discriminatory"
  • Liquidity demanders enter sequentially and:
    • "later" buyers pay more b/c of the price impact from "earlier"/faster entrants
  • Costs:
    • informed face the price impact cost
    • all pay transaction cost 
      • in terms of "asset" \(\to\) depends on trader's asset valuation

Model Recap: informed trader costs & choices

DEX

CEX

bid-ask spread cost (flat)

trans cost (flat)

+

marginal price (increases as informed trade on the same side)

\(\Rightarrow\) trade on DEX until the marginal price there = the "flat" ask (bid) on CEX

\(\Rightarrow\) informed trade on both exchanges 

Model Recap & Comments: noise trader costs & choices

DEX

CEX

bid-ask spread cost (flat)

trans cost (increases in the noise trader asset valuation)

+

marginal price (flat = fundamental)

\(\Rightarrow\) trade on DEX if the private asset valuation is sufficiently low (\(\to\) perceive the trans fee to be "low") & on CEX otherwise

\(\Rightarrow\) noise trade on both exchanges 

  • This assumption seems key, yet unclear where heterogeneity in private valuations comes from
  • Explore motives for trading on CEX vs DEX?
  • Differences in aspects other than the price?
  • E.g., custody?
    • \(\to\) trade exclusively on DEX because need tokens to use them in DeFi applications 
    • arguably these are "noise"
    • \(\to\) (?) expect more "noise" on DEX?

Model Recap & Comments: liquidity providers

DEX

CEX

Set the bid-ask spread to "break-even"

  • zero profits in expectation on CEX
  • there exists a liquidity pool size on DEX \(\to\) zero profits 
  • lose on the informed, profit from the "noise"

A knife-edge case?

Why only one level of the book?

  • The further in the queue, the more likely to trade against single-sided flow (informed)
  • Also, say, measure 1 of noise in total
    • \(\to\) if the queue position >0.5, you only get to trade against the informed!
    • \(\to\) must quote at the "new" fundamental

How critical is the non-discriminatory, no re-quoting LOB?

Comments on the Empirical Implications

informed trade on DEX until the marginal price = the ("fixed") ask/bid on CEX

  • Larger liquidity pool on DEX \(\to\) smaller price impact \(\to\) more informed on DEX \(\to\) better liquidity on CEX
    • Empirical implication #1 from the paper: adding a DEX improves CEX liquidity
    • Need a more detailed explanation here:
      • why wouldn't noise migrate from CEX to DEX after its intro (zero price impact on the DEX!) 
      • larger size isn't the same as going from "CEX only" to "CEX & DEX"

@katyamalinova

malinovk@mcmaster.ca

slides.com/kmalinova

https://sites.google.com/site/katyamalinova/

CBER Conference Discussion:"Coexisting Exchange Platforms: Limit Order Books and Automated Market Makers"

By Katya Malinova

CBER Conference Discussion:"Coexisting Exchange Platforms: Limit Order Books and Automated Market Makers"

CBER May 2022 Conference Discussion

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