2.6.1 One company, four jobs: the centralised exchange
Most crypto trading happens in an app that looks like a brokerage. Behind it, one company does the work that four separately regulated firms do in the markets of Session 2.1.
In Session 2.1 you followed an order through a broker, an exchange, a clearing house and a custodian: four firms, four rulebooks, each checking the others. A centralised exchange (CEX) such as Binance, Coinbase or OKX does all four jobs itself: it takes your order (broker), matches it in its own limit order book (venue), sets your margin and closes your position when it runs out (clearing house), and holds every coin and dollar you deposit (custodian). Many also lend, make markets or issue a token. IOSCO, the global body of securities regulators, lists "conflicts of interest arising from vertical integration of activities and functions" and "custody and client asset protection" among the six key areas of its 2023 crypto recommendations.
Once you deposit, the coins leave your control: your balance is a row in the exchange's database, and you cannot see what stands behind it. In the US, for example, SEC Rule 15c3-3 makes a broker-dealer keep customers' securities and cash segregated from its own, and UK and EU client-asset rules do the same; a crypto exchange's promise of segregation is only as good as whoever checks it.
| Job | Traditional market (Session 2.1) | Centralised exchange | Decentralised exchange |
|---|---|---|---|
| Take the order | a broker | the exchange's app or API | your wallet signs a transaction |
| Match buyer and seller | an exchange's order book | the exchange's own order book | a pool contract (§2.6.3) or an on-chain order book |
| Guarantee the trade, run margin | a central counterparty | the exchange's risk engine | rules written into the contract |
| Hold the assets | a custodian, segregated by law | the exchange's wallets, often pooled | you, until the trade settles |
| Who checks | regulators, auditors, the other three firms | mostly the exchange itself | anyone who reads the blockchain |
On a venue that does not segregate client assets — or where no one checks that it does — a CEX balance is in effect an unsecured promise from one company that also matches your trades and decides when to liquidate you. In crypto, custody risk and counterparty risk live inside the venue, so choosing where to trade is a risk decision, not a convenience.
Crypto trades every hour of every day, so this session annualises with 365 days (8,760 hours), not 252 (annualisation: Session 2.3). Prices differ across venues — Makarov and Schoar (2020) found large, recurring arbitrage gaps between exchanges, far larger across countries than within them — and volume needs a haircut: Cong et al. (2023) estimate wash trading at over 70% of reported volume on the unregulated exchanges they studied (manipulation is Session 15.6).
2.6.2 When the venue is the risk: custody, reserves & FTX
Custody risk and counterparty risk are two faces of one question: if this firm fails tomorrow, what do I get back? In November 2022, FTX's customers found out.
Custody risk is the risk of losing assets because of how, and by whom, they are held: stolen from a hot wallet, locked behind a lost key, or quietly used by the custodian. Counterparty risk is the risk that whoever owes you — a venue, an issuer, a borrower — does not pay. A clearing house caps counterparty risk at about one day's price move (Session 2.4); on a CEX both risks sit in one company, uncapped. Custody can also fail on its own: the FBI attributed the theft of about $1.5 billion of crypto from the exchange Bybit, on or about 21 February 2025, to North Korean hackers. Bybit stayed solvent and, with emergency loans, restored full backing of client assets within about three days (CNBC, 24 February 2025): the loss fell on the firm, not its customers.
Nine days in November
| Date (2022) | What happened |
|---|---|
| 2 Nov | CoinDesk reports that about $5.8 billion of the $14.6 billion of assets on the balance sheet of Alameda Research — the trading firm owned by FTX's founder, Sam Bankman-Fried — is tied to FTT, a token FTX itself issued. |
| 6 Nov | Binance's chief executive says Binance will sell its FTT holdings. Customers start pulling money off FTX. |
| 8 Nov | Binance announces a non-binding deal to buy FTX; later that day FTX suspends crypto withdrawals. |
| 9 Nov | Binance walks away, citing its due diligence and news reports of mishandled customer funds. |
| 11 Nov | FTX files for Chapter 11 bankruptcy in Delaware. |
Sources: CoinDesk (2 and 9 Nov 2022), CNBC (9 Nov 2022), and the FTX bankruptcy filings.
What failed was the separation of roles. The SEC alleged in December 2022 that FTX gave Alameda "a virtually unlimited 'line of credit' funded by the platform's customers" and exempted it from key risk controls — the clearing job waived for an insider, paid for by the custody job. John J. Ray III, the new chief executive, told the bankruptcy court he had never seen "such a complete failure of corporate controls". A jury convicted Bankman-Fried on all seven counts on 2 November 2023; he was sentenced to 25 years on 28 March 2024, and prosecutors said he had taken more than $8 billion of customers' money.
Under the plan confirmed on 7 October 2024 (CNBC), customers with claims up to $50,000 — most creditors by number — received about 120% of their allowed claims from 18 February 2025, and larger customer claims had received 105% by the fifth distribution on 31 July 2026 (FTX Recovery Trust). But the claims were fixed in dollars at 11 November 2022 prices, when bitcoin traded near $17,000: a customer who held bitcoin got dollars at the crash price, more than two years later. Counterparty loss is not only whether you are paid, but in what and when.
Proof of reserves, and what it cannot prove
After FTX, exchanges began publishing proof of reserves: their wallet addresses (the assets) plus a Merkle tree of customer balances (the liabilities) in which each customer can find their own. As Buterin (2022) sets out, it is a snapshot, not a stream; coins can be borrowed for the snapshot (exchanges could "shuttle collateral" between each other); other debts never enter the tree; and fiat still needs an auditor. In December 2022 the auditor Mazars paused its proof-of-reserves work for all crypto clients, citing how the public understood the reports.
Solvency means assets cover all liabilities all the time; proof of reserves shows certain coins in certain wallets at one moment. Unless you know the venue segregates client assets and someone checks that it does, treat a CEX balance as an unsecured loan to it: size it, spread it across venues, and withdraw what you are not using.
2.6.3 Decentralised exchanges & the constant-product AMM
A decentralised exchange replaces the company with a program. The most influential design has no order book at all — just two piles of tokens and one line of algebra.
A decentralised exchange (DEX) is a set of smart contracts — programs on a public blockchain — that you trade with straight from your own wallet. Most spot DEX volume runs through automated market makers (AMMs): instead of matching buyers with sellers, an AMM is a pool of two assets, funded by liquidity providers (LPs), that always trades against you at a formula price. Uniswap v2's pool (Adams, Zinsmeister & Robinson 2020) holds tokens and dollars of a stablecoin (§2.6.5) and accepts any trade that does not reduce the product of the reserves:
Sell tokens and the pool pays out the that keeps the product at . The fee — 0.30% on Uniswap v2, split 0.25% to LPs and 0.05% to the protocol since the "UNIfication" governance proposal was executed on 28 December 2025 (Uniswap documentation, checked 2026) — comes off what you pay in: only counts toward , but all of it stays in the pool, so grows with every trade:
Write the trade's size as a share of the pool, . Its total cost against the pre-trade price — fee plus market impact — is
That is the rule of thumb to keep: an AMM trade costs the fee plus roughly its own size as a share of the pool. The lab's pool holds 1,000 tokens and $2,000,000, a price of $2,000:
| Sell (share of pool) | Tokens | Worth at the pre-trade price | Average price received | Total cost (fee + impact) | Pool price after |
|---|---|---|---|---|---|
| 0.1% | 1 | $2,000 | $1,992.01 | 0.40% | $1,996.01 |
| 1% | 10 | $20,000 | $1,974.32 | 1.28% | $1,960.65 |
| 5% | 50 | $100,000 | $1,899.32 | 5.03% | $1,814.32 |
| 10% | 100 | $200,000 | $1,813.22 | 9.34% | $1,653.34 |
| 25% | 250 | $500,000 | $1,596.16 | 20.19% | $1,280.77 |
Depth is everything: the same $20,000 sale into a pool 10 times deeper costs 0.40% instead of 1.28%. The swap itself, from the lab:
def swap(amount_in, reserve_in, reserve_out, fee=FEE): eff = amount_in * (1.0 - fee) # only this part counts toward k out = reserve_out * eff / (reserve_in + eff) # keeps (reserve_in + eff)·(reserve_out − out) = k return out, reserve_in + amount_in, reserve_out - out # the whole input stays: k grows for s in SIZES: # 0.1%, 1%, 5%, 10%, 25% of the token reserve dx = s * X0 dy, x1, y1 = swap(dx, X0, Y0) exec_px = dy / dx cost = 1.0 - exec_px / mid0 assert abs(cost - sell_cost_closed_form(s)) < 1e-12
Your swap waits in a public queue before a validator puts it in a block, where anyone can read it. A bot can buy just before your purchase and sell just after — a "sandwich" — pocketing the impact you were about to cause. Value extractable by whoever orders the transactions is called MEV (Daian et al. 2020 coined "miner extractable value"): front-running with the order book replaced by a block. The first defence is a tight minimum output on every swap.
An AMM is a market maker (a business you met in Session 1.1) with a fixed quoting rule: it never widens its spread when it is being picked off. Session 14.1 builds the order book it replaces, Session 14.5 a market maker who manages inventory risk, and Session 6.5 prices slippage on any venue.
2.6.4 Liquidity providers & impermanent loss
Someone has to fill the pool. Liquidity providers earn the fees — and pay for them by taking the other side of every arbitrageur.
When the price elsewhere moves, arbitrageurs trade against the stale pool until it matches (Angeris et al. show why a constant-product pool must track the outside price) — which means the LP sells the token as it rises and buys it as it falls. Without fees the pool's state depends only on the price : and , so the LP holds . If the price moves by the ratio over years, compare that with holding the deposit:
That gap is impermanent loss — "impermanent" because it vanishes if the price returns, permanent once you withdraw. It is symmetric in the ratio: a halving and a doubling both cost −5.7% against holding, ±20% costs −0.6% or −0.4%, and a fourfold rise −20%. In the lab an arbitrageur makes 720 hourly trades against a pool on each of 40 simulated paths, using only the swap function, and the LP's result matches the formula to within 1e-15 on every path: only the final price matters.
How much does it cost on average? If the price has no drift, holding breaks even in expectation, but is concave, so the LP does not: for a lognormal price , with in years, and
At a crypto-like 80% volatility over one year, theory says −7.69%; 200,000 simulated years give −7.72% with a standard error of 0.035%. So fees must earn about 3.1% a year just to match holding at 50% volatility, 7.7% at 80% and 11.8% at 100% ( for one year).
The LP's payoff is concave, the shape an option seller holds (options arrive in Session 2.7). Providing liquidity is a bet that fees beat roughly σ²/8 a year. The loss goes to arbitrageurs trading against stale prices — the adverse selection every market maker faces, formalised by Milionis et al. (2022) as "loss-versus-rebalancing". Uniswap v3 (2021) lets LPs concentrate liquidity in a price range: more fees per dollar, more loss per move.
2.6.5 Stablecoins: four designs, four ways to break
Most crypto prices are quoted in a dollar that is not a dollar. How it is built decides how it breaks.
A stablecoin is a token designed to hold a fixed value, usually $1, by being a claim on something: an issuer's reserves, a pile of crypto collateral, a mechanism, or a hedged crypto position.
| Design (examples) | What stands behind $1 | How it breaks — and when it did |
|---|---|---|
| Fiat-backed (USDT, USDC) | cash, Treasury bills and bank deposits held by an issuer that redeems at par | USDC fell to roughly 87–88 cents on 11 March 2023, when $3.3 billion of its roughly $40 billion of reserves sat at the failed Silicon Valley Bank; it recovered once US authorities said on 12 March that all SVB depositors would be protected. |
| Crypto-collateralised (DAI) | more crypto than the stablecoins issued, locked in a contract that liquidates under-collateralised positions | A crash faster than the liquidations leaves the system short of collateral — and the collateral can itself depeg: DAI, then about half backed by USDC, hit 88 cents with it on 11 March 2023 (CoinDesk; Cointelegraph). |
| Algorithmic (UST, Terra) | a mint-and-burn swap with a sister token, and little outside collateral | A run began on 7 May 2022; Terra lost about $50 billion of value in three days (Liu, Makarov & Schoar 2023), and UST traded around 12 cents by 13 May (CNBC, citing CoinGecko). |
| Synthetic dollar (USDe, Ethena) | spot crypto plus a short perpetual — the funding trade of §2.6.7, packaged as a token | It breaks if funding stays negative long enough to drain its reserve, or if a venue holding the short fails. On 10 October 2025 it hit 65 cents on Binance's own order book while staying near $1 elsewhere; Binance priced collateral off that thin book, and accounts using it as margin were liquidated (CoinDesk). |
Read each design as something you already know. A fiat-backed coin is a narrow bank without a banking licence: it carries the credit risk of its reserves and issuer, and few firms can redeem directly — Tether let an average of six agents a month redeem for cash (Ma, Zeng & Zhang 2025). A crypto-collateralised coin is a margin loan with the liquidation rules in code. An algorithmic coin works while people believe it works; Terra's run was visible on-chain, which sped it up, and the wealthier, more sophisticated investors ran first and lost less (Liu, Makarov & Schoar 2023). A synthetic dollar is §2.6.7's basis trade in a wrapper, with that trade's risks.
It is a claim on an issuer, a contract or a mechanism, and it can trade below $1 exactly when you need it. Your "dollar" P&L is P&L in a token, and stablecoin collateral can be marked down — on one venue's prices — and liquidate a position that was otherwise fine. Haircut it, and know who can redeem at par.
2.6.6 Perpetual futures & the funding rate
The most traded instrument in crypto is a futures contract that never expires. With no expiry there is no convergence — so the venue builds one in, as a payment between longs and shorts every few hours.
In Session 2.4 a futures contract converges to spot because at expiry it is the asset. A perpetual future (a "perp") has no expiry. The idea is older than crypto — Shiller (1993) proposed perpetual contracts on hard-to-trade indices — but it took off when BitMEX introduced the first crypto perpetual in 2016 (He et al.), long offering up to 100× leverage (250× since April 2024, as reported by The Block). By one estimate, perps traded over $60 trillion in 2024 (Chitra 2025).
What replaces convergence is the funding rate. With perp price , spot and premium (π for premium), at each funding time every long pays every short the funding rate times the position's notional — or receives it when the rate is negative; the money moves between traders, not to the venue (Ackerer, Hugonnier & Jermann 2026 derive the resulting no-arbitrage prices). Binance publishes it for its default 8-hour interval, and Hyperliquid uses the same form paid hourly (checked 2026):
where is the premium averaged over funding interval and an "interest" component of 0.01% per 8 hours. While the average premium sits between −0.04% and 0.06%, funding is exactly — a built-in 10.95% a year from longs to shorts when nothing is happening. Outside that band funding follows the premium, so a gap costs the crowded side about the gap itself, every interval.
| Venue (as of 2026) | Funding interval | Notes |
|---|---|---|
| Binance, USDⓈ-margined perps | 8 hours by default (00:00, 08:00, 16:00 UTC) | may switch to 4 or 1 hour in extreme volatility |
| BitMEX | 8 hours (04:00, 12:00, 20:00 UTC) | the original crypto perp (2016) |
| Hyperliquid (on-chain) | every hour | same formula; capped at 4% an hour |
| Coinbase Derivatives (US, CFTC-regulated) | accrues hourly, settles twice a day | "perpetual-style": a five-year expiry; trading began 21 July 2025 |
What funding does to the premium: a toy model
The lab simulates 2,000 years of hourly trading, with spot at 60% volatility. Speculative demand pushes the premium — a steady long bias plus 2-basis-point hourly shocks, correlated 0.5 with spot because buyers chase rallies — and arbitrage, paid by funding, closes a fraction of the gap each hour (a 8-hour half-life):
The counterfactual switches funding off: nobody is paid to close the gap, , and the premium is a random walk with drift. The model assumes that funding-paid arbitrage closes of the gap each hour (the funding it computes never feeds back), so it illustrates the mechanism rather than testing it; both regimes match their theory. With funding, the premium after a year averages +0.021% (theory +0.020%) with a standard deviation of 0.049% (theory 0.050%), and 99% of paths sit within 0.14% of spot. Without it, the same shocks leave the perp 14.6% above spot on average, give or take 1.8%.
Funding was exactly in 72% of intervals and negative in 6%. A year of funding averaged 13.9% of notional (5th–95th percentile 12.5% to 15.4%), above the 10.95% that alone pays, because the premium averages 0.02%, above , so more intervals break out above the band — where funding follows the premium up — than below it.
Funding makes a gap expensive to hold and pays whoever closes it, but it cannot force convergence the way expiry does. He, Manela, Ross and von Wachter find perp prices stray further from their no-arbitrage values in crypto than comparable prices do in currency markets, though less over time. A perp tracks spot only as well as arbitrage capital is paid, and willing, to make it.
2.6.7 Basis trades, liquidation & auto-deleveraging
The funding that longs pay is income for somebody. Collecting it is the crypto basis trade — the cash-and-carry of futures, with two new ways to lose.
The trade
With a dated future it is the cash-and-carry of Session 2.4: buy spot, sell the future, and lock in the futures premium over spot, , whatever the price does. Crypto desks call that premium "the basis"; in 2.4's basis convention, , the same gap is negative, so check the sign. Crypto futures premiums often sit far above dollar interest rates: Schmeling, Schrimpf and Todorov (2023) document bitcoin and ether carry averaging above 10% a year and at times 60%, left on the table because arbitrage is risky "due to spikes in margins and liquidations amid drawdowns". Whether it is a risk premium is a question for Session 8.4.
With a perp you buy one unit of spot, short one unit of the perp and collect funding. The legs cancel except for the gap between them, so the year's gain is exactly
— funding received, minus any widening of the premium. After 0.20% of fees the trade earned 14.0% of starting notional on average (5th–95th percentile 6.9% to 23.9%, since the notional moves with the price) and 0% of paths lost money, while the spot leg alone had a standard deviation of 64%. With the short leg at 3×, capital is 1.33 times notional and the return on it 10.5% — assuming the short is topped up and never liquidated, and that funding stays as positive as this model makes it; real funding has turned negative for long stretches. It is not free money, for two reasons.
1 · The hedge leg can be liquidated. Hold the spot in cold storage and the short perp at 3× on an exchange, and a 32.7% rally liquidates the short while the offsetting gain sits in a wallet the exchange cannot see. In the lab that happens within a quarter on 29% of paths and within a year on 54%, leaving you long spot at the top of a rally. 2 · The venue can fail (§2.6.2). Assume, purely for illustration, a 2% annual failure probability with nothing recovered. If both legs sit on the failed venue, the expected return falls from 10.5% to 8.3%, and it breaks even at a failure probability of 9.5%; with the spot in cold storage only the margin, 25% of the capital, is at stake, and the expected return is 9.8%. The average is not the problem; the loss tail is.
How a crypto venue liquidates you
Liquidation is the forced closing of a position by the venue when its margin runs out. In Session 2.4 a margin call asked you for cash, and the position was closed only if you could not pay. A crypto venue checks equity against the maintenance margin continuously, on a mark price built from spot indices rather than its own last trade, and there is no call: the engine takes over. For an isolated-margin long with leverage and maintenance rate (a fraction of the current notional), that happens when the price falls to
— almost exactly the of Session 2.4. Then comes a waterfall (fig 2.6.7). At the bankruptcy price the position's equity is exactly zero. If the engine sells before it, part of the leftover margin feeds an insurance fund as a fee; if the price gaps through it, the fund absorbs the loss; and if the fund runs dry, auto-deleveraging (ADL) closes profitable positions on the other side, ranked by profit and leverage (Binance's auto-deleveraging FAQ).
On 10 October 2025 more than $19 billion of leveraged crypto positions were liquidated within 24 hours, the largest such day on record (CoinDesk Research), and on the on-chain venue Hyperliquid, ADL closed $2.1 billion of positions in 12 minutes (Chitra 2025): traders who had been right had their winners shut.
How long does a leveraged position last?
The lab simulates 20,000 one-year hourly paths in calendar time at 60% volatility, no drift and a 0.5% maintenance margin; the first breach liquidates. Real engines check more often than hourly, so these slightly understate.
| Leverage | Fall that liquidates, d* | Liquidated within 1 day | within 30 days | within 1 year | Median time to liquidation |
|---|---|---|---|---|---|
| 3× | 33.0% | 0.0% | 2.3% | 60.7% | 243 calendar days |
| 10× | 9.5% | 0.1% | 57.9% | 90.3% | 21 calendar days |
| 25× | 3.5% | 21.4% | 83.5% | 96.5% | 81 hours |
| 100× | 0.5% | 78.2% | 96.5% | 99.2% | 4 hours |
These match the barrier-crossing formula of Session 2.4, corrected for hourly checks, within four standard errors (largest gap 1.7) wherever the liquidation price is at least five hourly standard deviations (0.64% each) away: up to 25× here. (Monte Carlo is Session 3.5.)
A basis trade has no price exposure only while both legs survive and both venues pay. Size the short leg for the rally you can fund (Session 2.4's lesson), keep collateral where the margin is, and count venue failure as a cost.
2.6.8 The risk stack & regulation
Traditional markets hide most of these risks behind law, institutions and a closing bell. In crypto they are all on your side of the screen, stacked under every position you hold.
Regulation, as of September 2026
Rules differ by jurisdiction and are changing fast; these are dated examples, not advice.
| Jurisdiction | Where things stand |
|---|---|
| European Union | MiCA (Regulation (EU) 2023/1114). Its stablecoin rules have applied since 30 June 2024 and its rules for crypto-asset service providers since 30 December 2024. National transitional periods ended by 1 July 2026: a firm serving EU clients now needs a MiCA authorisation (ESMA). |
| United States | The GENIUS Act, signed on 18 July 2025, created a federal regime for payment stablecoins, with at least $1 of permitted reserves for each $1 issued; it takes effect on the earlier of 18 January 2027 (18 months after enactment) or 120 days after regulators issue final rules. There is no comprehensive market-structure law: the House passed the CLARITY Act in July 2025, but a Senate cloture vote on it failed on 15 September 2026. Meanwhile the SEC approved spot bitcoin exchange-traded products on 10 January 2024, CFTC-regulated "perpetual-style" futures have traded since July 2025, and states license exchanges — New York's BitLicense dates from 2015. |
| United Kingdom | The FCA's new cryptoasset regime is expected to come into force on 25 October 2027; firms can apply from 30 September 2026. |
For a quant, regulation changes the bottom of the risk stack — an authorised venue must segregate client assets and publish its rules — not the top.
2.6.9 Try it
Open the companion lab, predict before you run, and check your prediction against the asserts.
1. In section 1 set FEE = 0.0005. Predict the cost of the 1% sale from , then run: how much of the old cost was the fee?
2. In section 2 set IL_SIGMA = 0.5 and predict the expected loss against holding from ; the Monte Carlo assert tells you if you were right.
3. In section 5 add 20 to LEVELS (keep the list sorted). Compute d* by hand from , then read the median time to liquidation off the printed table.
Success: each prediction matches the lab, and you can say in one sentence why survival time falls so much faster than d*.
2.6.10 Glossary · Check yourself · Go deeper
Check yourself
1. Your exchange halts withdrawals and files for bankruptcy while holding your bitcoin. Which two risks just materialised, and what did FTX's customers get back?
2. You sell 100 tokens into the lab's pool of 1,000 tokens and $2,000,000. What does it cost, and what would help?
3. You deposit $10,000 as a liquidity provider when the token is at $2,000. It doubles. Ignoring fees, how do you compare with someone who simply held the deposit?
4. A perp's premium averaged 0.10% over an 8-hour interval. What is the funding rate, who pays it, and what does it add up to if it lasts a year? What would you do?
5. You run the basis trade with spot in cold storage and a 3× short perp on an exchange. The price rallies 35% in a week. What happens, and how should you have set it up?
6. A friend trades 25× longs "with a tight stop". How far can the price fall before liquidation, and how does that compare with an ordinary day?
1. Price the LP's risk. Run section 2 with IL_SIGMA at 0.5, 0.8 and 1.0 and tabulate the Monte Carlo loss against ; at 80% volatility, what daily volume (as a share of the pool) lets the 0.25% LP fee break even?
2. Stress the funding loop. In section 3 set CORR_DEMAND = 0.9 and MEAN_PREM = 0.0004. How do the share of intervals at ι, the negative share and the annual funding change? Explain it with the clamp.
3. Move the maintenance margin. In section 5 set M_RATE = 0.01. Which leverages change most, and why does 100× become almost instant?
4. Read Buterin's proof-of-solvency post and write three sentences on what proof of reserves would and would not have revealed about FTX in October 2022.
5. For next time: keep your sketch of fig 2.6.4; the payoff diagrams of Session 2.7 will name its shape.
📚 Go deeper
- Adams, H., Zinsmeister, N. & Robinson, D. (2020). "Uniswap v2 Core." Whitepaper, March 2020. https://app.uniswap.org/whitepaper.pdf
- Milionis, J., Moallemi, C. C., Roughgarden, T. & Zhang, A. L. (2022). "Automated Market Making and Loss-Versus-Rebalancing." arXiv:2208.06046
- He, S., Manela, A., Ross, O. & von Wachter, V. (2022, revised 2026; version 7 of 17 September 2026). "Fundamentals of Perpetual Futures." arXiv:2212.06888
- Schmeling, M., Schrimpf, A. & Todorov, K. (2023). "Crypto Carry." BIS Working Papers No. 1087. https://www.bis.org/publ/work1087.htm
- Liu, J., Makarov, I. & Schoar, A. (2023). "Anatomy of a Run: The Terra Luna Crash." NBER Working Paper 31160 (April 2023; since published in the Journal of Financial Economics, vol. 184). doi:10.3386/w31160
- Buterin, V. (2022). "Having a safe CEX: proof of solvency and beyond." 19 November 2022. https://vitalik.eth.limo/general/2022/11/19/proof_of_solvency.html
- Makarov, I. & Schoar, A. (2020). "Trading and Arbitrage in Cryptocurrency Markets." Journal of Financial Economics 135(2), 293–319. doi:10.1016/j.jfineco.2019.07.001
Sources for the numbers
- Adams, H., Zinsmeister, N., Salem, M., Keefer, R. & Robinson, D. (2021). "Uniswap v3 Core." Whitepaper, March 2021. https://app.uniswap.org/whitepaper-v3.pdf · Uniswap developer documentation, "Fees" (checked 2026). https://developers.uniswap.org/docs/get-started/concepts/fees · Uniswap governance, "UNIfication" (proposal 93, executed 28 December 2025). https://vote.uniswapfoundation.org/proposals/93
- Angeris, G., Kao, H.-T., Chiang, R., Noyes, C. & Chitra, T. (2019, revised 2021). "An analysis of Uniswap markets." arXiv:1911.03380
- Daian, P., Goldfeder, S., Kell, T., Li, Y., Zhao, X., Bentov, I., Breidenbach, L. & Juels, A. (2020). "Flash Boys 2.0: Frontrunning in Decentralized Exchanges, Miner Extractable Value, and Consensus Instability." IEEE Symposium on Security and Privacy. arXiv:1904.05234
- Shiller, R. J. (1993). "Measuring Asset Values for Cash Settlement in Derivative Markets: Hedonic Repeated Measures Indices and Perpetual Futures." Journal of Finance 48(3), 911–931. doi:10.1111/j.1540-6261.1993.tb04024.x
- Ackerer, D., Hugonnier, J. & Jermann, U. (2026). "Perpetual Futures Pricing." Mathematical Finance. doi:10.1111/mafi.70018
- Chitra, T. (2025, revised 2026). "Autodeleveraging: Impossibilities and Optimization." arXiv:2512.01112
- Cong, L. W., Li, X., Tang, K. & Yang, Y. (2023). "Crypto Wash Trading." Management Science 69(11), 6427–6454. doi:10.1287/mnsc.2021.02709
- Ma, Y., Zeng, Y. & Zhang, A. L. (2025). "Stablecoin Runs and the Centralization of Arbitrage." NBER Working Paper 33882. https://www.nber.org/papers/w33882
- IOSCO (2023). "Policy Recommendations for Crypto and Digital Asset Markets: Final Report." FR11/2023, 16 November 2023. https://www.iosco.org/library/pubdocs/pdf/IOSCOPD747.pdf
- SEC Rule 15c3-3, "Customer protection — reserves and custody of securities." 17 CFR 240.15c3-3. https://www.ecfr.gov/current/title-17/chapter-II/part-240/subpart-A/subject-group-ECFR541343e5c1fa459/section-240.15c3-3
- FTX: Allison, I. (CoinDesk, 2 Nov 2022) and CoinDesk timeline (9 Nov 2022) https://www.coindesk.com/layer2/2022/11/09/8-days-in-november-what-led-to-ftxs-sudden-collapse · CNBC, "Binance backs out of FTX rescue" (9 Nov 2022) https://www.cnbc.com/2022/11/09/binance-backs-out-of-ftx-rescue-leaving-the-crypto-exchange-on-the-brink-of-collapse.html · Declaration of John J. Ray III, In re FTX Trading Ltd., Case 22-11068 (Bankr. D. Del., 17 Nov 2022) https://www.documentcloud.org/documents/26141228-affidavitdeclaration-in-support-of-first-day-motion-declaration-of-john-j-ray-iii-in-support-of-chapter-11-petitions-and-first-day-pleadings-filed-by-ftx-trading-ltd/
- SEC press release 2022-219 (13 Dec 2022) https://www.sec.gov/newsroom/press-releases/2022-219 · US Attorney's Office, SDNY, "Samuel Bankman-Fried Sentenced To 25 Years In Prison" (28 Mar 2024) https://www.justice.gov/usao-sdny/pr/samuel-bankman-fried-sentenced-25-years-prison · CNBC, "Sam Bankman-Fried found guilty on all seven criminal fraud counts" (2 Nov 2023) https://www.cnbc.com/2023/11/02/sam-bankman-fried-found-guilty-on-all-seven-criminal-fraud-counts.html
- CNBC, "FTX bankruptcy judge approves more than $14 billion payback plan" (7 Oct 2024) https://www.cnbc.com/2024/10/07/ftx-bankruptcy-judge-approves-more-than-14-billion-payback-plan.html · FTX Recovery Trust, "FTX Announces Fifth Distribution of Approximately $900 Million to Creditors on July 31, 2026" (PR Newswire, 17 Jul 2026) https://www.prnewswire.com/news-releases/ftx-announces-fifth-distribution-of-approximately-900-million-to-creditors-on-july-31-2026-302828726.html · FTX, "FTX Announces Initial Distribution Date of February 18, 2025 for Convenience Class Creditors" (PR Newswire, 7 Feb 2025) https://www.prnewswire.com/news-releases/ftx-announces-initial-distribution-date-of-february-18-2025-for-convenience-class-creditors-302371626.html · Cointelegraph, "FTX debtors assess value of crypto claims based on petition date market prices" (16 Dec 2023) https://cointelegraph.com/news/ftx-reorganization-plan-crypto-assets-bankruptcy
- CoinDesk, "Auditing Firm Mazars Pauses Proof-of-Reserves Work for Crypto Clients" (16 Dec 2022) https://www.coindesk.com/business/2022/12/16/binance-proof-of-reserves-auditor-mazars-pauses-all-work-for-crypto-clients · FBI, "North Korea Responsible for $1.5 Billion Bybit Hack" (26 Feb 2025) https://www.ic3.gov/psa/2025/psa250226 · CNBC, "Crypto exchange Bybit says it fully replenished reserves after record $1.5 billion hack" (24 Feb 2025) https://www.cnbc.com/2025/02/24/bybit-replenished-reserves-after-record-breaking-1point5-billion-hack.html
- USDC, DAI and SVB: CoinDesk, "DAI Depegs to Lifetime Lows as Stablecoin Rout Plagues Crypto" (11 Mar 2023) https://www.coindesk.com/markets/2023/03/11/dai-depegs-as-stablecoin-rout-plagues-crypto · Cointelegraph, "Circle's USDC instability causes domino effect on DAI, USDD stablecoins" (11 Mar 2023) https://cointelegraph.com/news/circle-s-usdc-instability-causes-domino-effect-on-dai-usdd-stablecoins · CoinDesk (11 Mar 2023) https://www.coindesk.com/business/2023/03/11/circle-confirms-33b-of-usdcs-cash-reserves-stuck-at-failed-silicon-valley-bank · CNN (11 Mar 2023) https://www.cnn.com/2023/03/11/business/stablecoin-circle-silicon-valley-bank · Joint statement by the Treasury, Federal Reserve and FDIC (12 Mar 2023) https://www.federalreserve.gov/newsevents/pressreleases/monetary20230312b.htm
- UST: CNBC, "Cryptocurrency luna crashes to $0 as UST falls further from dollar peg" (13 May 2022) https://www.cnbc.com/2022/05/13/cryptocurrency-luna-crashes-to-0-as-ust-falls-from-peg-bitcoin-rises.html · USDe: Godbole, O., "No, Ethena's USDe Didn't De-peg During Friday's Crash" (CoinDesk, 13 Oct 2025) https://www.coindesk.com/markets/2025/10/13/no-ethena-s-usde-didn-t-de-peg
- Funding and liquidation rules (checked 2026): Binance, "Introduction to Binance Futures Funding Rates" https://www.binance.com/en/support/faq/360033525031 · Binance, "Binance Futures Liquidation Protocols", "Introduction to Futures Insurance Funds" and "What Is Auto-Deleveraging (ADL) and How Does It Work?" https://www.binance.com/en/support/faq/360033525471 https://www.binance.com/en/support/faq/binance-futures-liquidation-protocols-360033525271 https://www.binance.com/en/support/faq/introduction-to-futures-insurance-funds-360033525371 · Hyperliquid Docs, "Funding" https://hyperliquid.gitbook.io/hyperliquid-docs/trading/funding · BitMEX, "Perpetual Contracts Guide" https://www.services.bitmex.com/app/perpetualContractsGuide · Coinbase, "US Perpetual-Style Futures 101" https://www.coinbase.com/learn/futures/us-perpetual-style-futures-101
- BitMEX leverage: The Block, "BitMEX's bitcoin perpetual swap now offers 250x leverage ahead of halving" (19 Apr 2024) https://www.theblock.co/post/289766/bitmexs-bitcoin-perpetual-swap-250x-leverage-halving
- 10 October 2025: CoinDesk Research, "Market Spotlight: Inside Crypto's $19 Billion Liquidation Event" (17 Oct 2025) https://www.coindesk.com/research/market-spotlight-the-19-billion-liquidation-that-shook-crypto
- Regulation: Regulation (EU) 2023/1114 (MiCA) https://eur-lex.europa.eu/eli/reg/2023/1114/oj · ESMA, "Statement on the end of transitional periods under MiCA" (2026) https://www.esma.europa.eu/sites/default/files/2026-04/ESMA75-113276571-1679_Statement_on_the_end_of_transitional_periods_under_MiCA.pdf · CRS Insight IN12553, "Stablecoin Legislation: An Overview of the GENIUS Act of 2025 (P.L. 119-27)" https://www.congress.gov/crs-product/IN12553 · A&O Shearman, "The GENIUS Act: transforming US stablecoin regulation" (21 Jul 2025; effective date) https://www.aoshearman.com/en/insights/ao-shearman-on-fintech-and-digital-assets/the-genius-act-transforming-us-stablecoin-regulation · CoinDesk, "Crypto Clarity Act flames out in failed U.S. Senate vote" (15 Sep 2026) https://www.coindesk.com/policy/2026/09/15/crypto-clarity-act-flames-out-in-failed-u-s-senate-vote · SEC, Chair Gensler's statement on spot bitcoin ETPs (10 Jan 2024) https://www.sec.gov/newsroom/speeches-statements/gensler-statement-spot-bitcoin-011023 · NYDFS, virtual currency businesses (BitLicense) https://www.dfs.ny.gov/virtual_currency_businesses · FCA, "A new regime for cryptoasset regulation" (updated 22 Sep 2026) https://www.fca.org.uk/firms/new-regime-cryptoasset-regulation
Educational material only — not investment, legal or tax advice. Backtests and simulations are hypothetical. Disclaimer · Text CC BY 4.0 · Code MIT.