Chaos and Order

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Prologue — Into the `<10ns` world

In 2026, a microwave-wireless hop between the Chicago Mercantile Exchange (CME) and the NY4 datacenter in New Jersey clocks roughly `4.7ms`; fiber takes `7.2ms`. To capture those `2.5ms`, a chain of antenna towers cuts across the Illinois corn belt. The operators are Jump Trading's subsidiary World Class Wireless, McKay Brothers, and New Line Networks. A single route can lease for more than `$10M` per year.

Inside the exchange, the unit changes again. CME Globex matches in `~10μs` on average, and gateway round-trip is `<100μs`. HFT firms cut that further with custom FPGAs. Optiver's Verilog team built an options quoting engine that reacts to a new quote in `<500ns`. Hudson River Trading aligns its matching-engine simulator data structures at `<10ns` granularity.

This is the lay of that land — Citadel Securities, Two Sigma, Jane Street, Optiver, Jump, Virtu, IMC, Tower, Hudson River, Flow Traders, DRW — and Korea's NH Investment & Securities, Mirae Asset, Kiwoom, plus Japan's Nomura, MUFG, SBI and Daiwa algo desks.

1. What HFT actually means — definition and misconceptions

HFT is not a single strategy but a combination: microsecond decision-making, automated order routing, and proprietary capital. The SEC's 2014 staff report defined HFT by four traits.

| Trait | Description |

| --- | --- |

| Proprietary capital | Trades on firm capital, not customer money |

| Very short holding periods | Intraday, often milliseconds |

| Frequent order/cancel | Fill ratios commonly below 1% |

| Direct market access | DMA + co-location + private lines |

A common confusion is the line with **algorithmic trading**. Algo trading is broader and includes execution algorithms from Goldman/Morgan/UBS (VWAP, TWAP, IS). HFT is the subset that adds proprietary capital, ultra-low latency and short holding periods. Korean "algorithmic trading" desks at NH ETF LPs and Mirae Asset arbitrage are squarely HFT.

2. Market microstructure — LOB, tick size, queue priority

Every HFT strategy runs on top of the **Limit Order Book (LOB)** — a queue of buy and sell quotes sorted by price-time priority. Same price, earlier order, fills first.

ASK SIDE BID SIDE

$100.05 | 500 $99.95 | 1000

$100.04 | 1200 $99.94 | 800

$100.03 | 300 $99.93 | 2500 <-- best bid

$100.02 | 800 <-- best ask

spread = $100.02 - $99.93 = $0.09 (9 ticks @ tick=$0.01)

Three variables matter most.

- **Tick size.** US equities are `$0.01` by default, `$0.0001` for sub-$1 names. The SEC's 2024 variable-tick rule trimmed some ETFs to `$0.005`.

- **Queue priority.** At the same price, earlier in the queue means higher fill probability. HFT firms race to be first in line at each new price level.

- **Order types.** Limit, Market, IOC, FOK, Hidden, Iceberg, Peg, Mid-point. They differ across exchanges, and those differences are themselves a source of edge.

3. Citadel Securities — apex market maker

[Citadel Securities](https://www.citadelsecurities.com/) was founded by Ken Griffin in Chicago in 2002. Legally separate from the Citadel hedge fund, the market-making sister reported `$23B` revenue and more than `$10B` operating income in 2024 — a single firm that intermediates ~25% of US equity volume, ~30% of US options, and over 40% of US retail order flow.

The business stands on four pillars.

- **US equity market-making.** NYSE/Nasdaq DMM (Designated Market Maker).

- **US options market-making.** CBOE / Nasdaq Options.

- **Retail order flow.** Internalizes flow from Robinhood, Charles Schwab, E*TRADE, Webull via Payment-for-Order-Flow.

- **Treasuries / rates.** A top non-bank market maker in US Treasuries.

Citadel Securities' edge is **cross-asset hedging**: the same firm makes markets in SPY, S&P 500 futures and all 500 constituents at once, so it can hedge an ETF buy with a fraction of a futures contract and a slice of constituents simultaneously.

4. Jane Street — King of ETFs, King of OCaml

[Jane Street](https://www.janestreet.com/) launched in New York in 1999. Estimated 2024 revenue: `$20B+`; operating income near `$14B`. About 2,500 staff, of which 70%+ are traders or engineers, and it hires top math/CS talent from Columbia, MIT and Harvard with almost no marketing.

Two things set Jane Street apart.

- **#1 in US ETF market-making.** From megacaps like SPY/IVV/QQQ to single-stock ETFs, Jane Street holds around 30% of US ETF AP (Authorized Participant) activity. It was the lead market maker on the spot Bitcoin ETFs (IBIT, FBTC) when they launched in early 2024.

- **OCaml**. The entire codebase is in OCaml — by 2025 it exceeded 30 million lines. ETP (Exchange Trade Pad — Jane Street's trader workstation), the risk engine, and the signal pipelines are all OCaml.

(* Jane Street style OCaml HFT pseudo — options theo vs market *)

open Core

open Async

module Quote = struct

type t =

{ symbol : string

; bid : float

; ask : float

; bid_size : int

; ask_size : int

; ts : Time_ns.t

}

[@@deriving sexp]

end

let theoretical_price ~spot ~strike ~rate ~vol ~ttm =

(* Black-Scholes call (simplified) *)

let open Float in

let d1 = (log (spot / strike) + ((rate + (0.5 * vol * vol)) * ttm))

/ (vol * sqrt ttm) in

let d2 = d1 - (vol * sqrt ttm) in

(spot * Cdf.standard_normal d1)

- (strike * exp (-. rate * ttm) * Cdf.standard_normal d2)

let edge_signal (q : Quote.t) ~theo =

let mid = (q.bid +. q.ask) /. 2.0 in

let edge = theo -. mid in

if Float.abs edge > 0.02 then `Trade edge else `Skip

The OCaml rationale, quoted often: type safety catches accounting bugs at compile time, pattern matching expresses market protocols cleanly, and GC behavior is predictable. The firm contributes OCaml compiler patches upstream and is the leading sponsor of MirageOS.

5. Two Sigma — a statistics and ML house

[Two Sigma](https://www.twosigma.com/) was founded in New York in 2001. AUM around `$60B+` in 2025. Co-founder David Siegel came out of the MIT AI Lab, John Overdeck from Amazon; they met at D.E. Shaw and split off.

Highlights.

- **Classified as a systematic hedge fund**, more "mid-frequency statistical arbitrage" than pure HFT. But the firm also runs market-making and short-horizon signal desks, so it belongs to the broader HFT ecosystem.

- **Data-centric**. Early adopter of alternative data — satellite imagery, credit card transactions, location data, news sentiment.

- **Engineering culture**. Sponsors Spark/Kafka conferences and ships its own ML stack (BeakerX, Two Sigma Platform).

Two Sigma also owns **Two Sigma Securities**, a separate market-making subsidiary in US equities and options — the #4 non-bank market maker behind Citadel, Virtu and Jane Street.

6. Optiver — options out of Amsterdam

[Optiver](https://optiver.com/) was founded in Amsterdam in 1986. Operating income in 2024 above `$5B`, headcount around 2,000. Offices in Chicago, Sydney, Shanghai, Taipei, Mumbai and London.

The specialty is **options market-making**. Optiver is a registered market maker on virtually every major option venue (Eurex, CBOE, ASX, KRX, OSE, TSE). In 2026, it is among the top five foreign market makers on KRX KOSPI 200 options.

Optiver's engineering color.

- **C++**. The core trading system is C++ with heavy template metaprogramming — Greeks are unrolled at compile time.

- **FPGA-first.** Chicago and Sydney use Xilinx FPGAs for option quoting, with `<500ns` reaction times.

- **Math-heavy hiring.** Former IMO team members are common; interviews lean on card-counting and medallion-trading simulations.

7. Jump Trading — Chicago's silent giant

[Jump Trading](https://www.jumptrading.com/) was founded in Chicago in 1999. Exact revenue is private, but 2024 estimates land around `$4–5B`. Headcount around 800–1,000. The firm trades US futures (especially grains, metals and rates), US bonds, FX, and crypto via Jump Crypto.

Jump pioneered microwave wireless networks. Subsidiary **World Class Wireless** operates lines between Chicago and Aurora and earns sizable revenue leasing the same routes to competitors. Jump benefits most directly from data arbitrage between CME and the New Jersey equity datacenters.

Another defining trait: Jump is a heavyweight in crypto. Jump Crypto is a major funder and validator on Solana, and previously operated the Wormhole bridge — covering roughly `$320M` of losses from its own capital after the 2022 exploit.

8. Virtu Financial — the firm the book changed

[Virtu Financial](https://www.virtu.com/) was founded in 2008 and IPO'd on the NYSE in 2015. 2024 revenue near `$2.5B`, operating income about `$700M`. Two engines: market-making and execution services (agency brokerage).

Virtu became a household name through Michael Lewis's *Flash Boys* (2014). The book lionized IEX's "speed bump" and painted HFT in a critical light, delaying Virtu's IPO by nearly a year. Ironically, the famously cited "Virtu had only 5 losing days in 5 years" line ended up advertising its risk management.

Acquiring KCG Holdings for roughly `$1.4B` in 2017 cemented Virtu as one of the big four US equity market makers (with Citadel, Jane Street, Two Sigma Securities).

9. IMC Trading, Tower Research, Hudson River, Flow Traders, DRW

Beyond the top four, this second tier is essential to the HFT industry.

| --- | --- | --- | --- |

- **IMC** shares a lineage with Amsterdam options market makers like Interactive Brokers' Thomas Peterffy. Major hubs in Chicago, Sydney, Mumbai.

- **Tower Research** entered KRX (Korea), NSE (India) and OSE (Japan) early. In the 2010s it was, by some measures, the #1 foreign market maker on KRX.

- **Hudson River Trading** self-reports trading 5–10% of US equity volume; hiring leans CMU / MIT / Stanford.

- **Flow Traders** is one of the two leading European ETF market makers and saw revenue spike after the 2024 spot Bitcoin ETFs.

- **DRW** mixes rates and futures with Cumberland (crypto OTC) and is the most diversified Chicago prop firm.

10. Latency arbitrage — the business of time

**Latency arbitrage** exploits the brief windows in which the same asset is quoted at different prices across venues. For a microsecond, SPY can be offered at `$500.01` on NYSE Arca while bid at `$500.02` on Nasdaq. Buying on Arca and simultaneously selling on Nasdaq is the trade.

The point is to receive market data and submit orders **before competitors**. So firms spend astronomically on:

- Exchange co-location racks (`$10K–30K` / month / rack).

- Direct market data feeds (NYSE Pillar, Nasdaq TotalView-ITCH, CME MDP 3.0) to receive ticks tens of microseconds earlier than the consolidated SIP.

- Microwave wireless and ULL fiber.

- FPGA gateways that handle packets directly from the NIC.

The SEC's stance is that latency arbitrage costs get absorbed into market-making and ultimately tighten spreads. Venues like IEX disagree and add a 350μs speed bump to neutralize it.

11. Statistical arbitrage — the statistics edge

**Statistical arbitrage** bets on statistical relationships between assets (cointegration, mean reversion, pair trading, factors) rather than single-asset inefficiency. Horizons stretch from minutes to days, so pure HFT it is not — but Two Sigma / Citadel / Jump stat-arb desks all sit on HFT infrastructure, so we group them here.

Typical stat-arb signals.

- **Cointegrated pairs.** KOSPI 200 mini-futures vs ETF, SPY vs ES futures.

- **Index reconstitution arbitrage.** Buying constituents ahead of Russell rebalancing day before AP demand arrives.

- **Seasonality.** Corn-futures patterns around USDA report releases.

- **Factor rotation.** Fama-French five factor, momentum, low-volatility.

/ kdb+/q example: 30-min cointegration z-score on two symbols

spread: select time, sym, px from quotes where sym in `KOSPI200`KS200ETF

joined: spread[`KOSPI200] - spread[`KS200ETF]

mu: 30 mavg joined

sigma: 30 mdev joined

z: (joined - mu) % sigma

/ z > 2 -> short joined, z < -2 -> long joined

kdb+/q is a columnar in-memory DB plus functional language designed by Arthur Whitney in 1993. Goldman / Morgan / JPM fixed income desks and nearly every HFT firm use it for time-series analytics.

12. ETF arbitrage — the bread and butter of Jane Street, Flow Traders, IMC

ETFs profit when the equation "constituent value = NAV" breaks. If the ETF trades above NAV, **Authorized Participants (APs)** buy constituents and create new ETF shares; below NAV, they redeem ETF shares for constituents and sell those.

That mechanism is what keeps ETFs near NAV — and to market makers it is near-riskless arbitrage. When the 2024 spot Bitcoin ETFs launched, the AP roster (Jane Street, Cantor Fitzgerald, Virtu) was an enormous beneficiary.

Why Jane Street rules ETFs comes down to one thing: the more complex the ETF (EM bond ETFs, single-country ETFs), the more decisive the AP's infrastructure. Jane Street's OCaml ETP was built early and built right.

13. Options market-making — Optiver, Citadel, IMC

Option market-making faces different challenges from equities.

- **Dimensionality explodes.** A single name like AAPL has hundreds of expiries, hundreds of strikes, calls and puts — thousands of order books. Market makers price all of them.

- **Greeks.** Delta, Gamma, Theta, Vega, Rho are computed in real-time to manage portfolio risk.

- **Volatility surface.** Implied vol per strike and expiry is fitted into a smooth surface and updated on every new tick.

- **Retail vs maker flow imbalance.** SPX options are mostly market makers; meme stock options carry heavy retail flow.

// C++ template metaprogramming - compile-time option Greeks

template <typename Greek, int N>

struct Surface {

std::array<std::array<Greek, N>, N> data;

constexpr Greek interpolate(double k, double t) const {

int i = static_cast<int>(k * N);

int j = static_cast<int>(t * N);

return data[i][j];

}

};

template <typename Quote>

inline auto theo(const Quote& q,

const Surface<double, 64>& vol_surf) {

const double k = q.strike / q.spot;

const double t = q.ttm;

const double sigma = vol_surf.interpolate(k, t);

return black_scholes(q.spot, q.strike, q.rate, sigma, q.ttm);

}

Optiver, Citadel, IMC, Susquehanna and CTC are the US options top-five. In 2026, Optiver and IMC also lead foreign market-making on KRX KOSPI 200 options.

14. Co-location + microwave wireless

Putting your own servers inside an exchange datacenter is **co-location**. Major datacenters today:

- **CME Globex**: Aurora, Illinois — about `1,200km` from NJ4.

- **NYSE Pillar**: Mahwah, NJ.

- **Nasdaq INET**: Carteret, NJ.

- **CBOE**: Chicago plus Secaucus.

- **Eurex**: near Frankfurt at Equinix FR2.

- **KRX**: Busan (next-generation system) + Yeouido, Seoul.

- **JPX (Tokyo)**: TSE's own datacenter, running arrowhead.

Co-lo cabinets are equidistantly cabled to ensure equal cable length, but at microsecond scale equality is only the floor — the real competition is faster NICs and faster matching-engine responses.

Microwave wireless beats fiber because light goes straight at almost the speed of light, while fiber's index of refraction slows it to ~67%. McKay Brothers, Quincy Data, and World Class Wireless (Jump's subsidiary) lease these routes.

15. FPGA acceleration — Solarflare and AMD Xilinx

CPUs introduce microsecond-scale jitter from cache misses and context switches. FPGAs essentially eliminate that jitter and process packets directly from the NIC, bypassing the OS and kernel stack.

Two industry stacks dominate.

- **Solarflare/Xilinx Onload + ef_vi.** A kernel-bypass library; Xilinx acquired Solarflare in 2019, AMD acquired all of Xilinx in 2022.

- **Mellanox/NVIDIA Connect-X + DPDK.** NVIDIA acquired Mellanox in 2020. RoCE (RDMA over Converged Ethernet) covers inter-node fabric.

FPGAs are used for:

- **Market data decoding.** Parsing multicast feeds like CME MDP 3.0 and Nasdaq ITCH directly on FPGA.

- **Tick-to-trade.** Market data in → decision → order out, all on a single chip.

- **Risk checks.** Capital limits, position limits, fat-finger checks before orders leave for the exchange.

// Simplified matching-engine FPGA snippet (price priority)

module match_engine (

input wire clk,

input wire [31:0] new_price,

input wire [15:0] new_qty,

input wire is_buy,

output reg [31:0] trade_price,

output reg [15:0] trade_qty,

output reg trade_valid

);

reg [31:0] best_bid, best_ask;

reg [15:0] bid_qty, ask_qty;

always @(posedge clk) begin

trade_valid <= 1'b0;

if (is_buy && new_price >= best_ask) begin

trade_price <= best_ask;

trade_qty <= (new_qty < ask_qty) ? new_qty : ask_qty;

trade_valid <= 1'b1;

end else if (!is_buy && new_price <= best_bid) begin

trade_price <= best_bid;

trade_qty <= (new_qty < bid_qty) ? new_qty : bid_qty;

trade_valid <= 1'b1;

end

endmodule

Optiver, Jump, Hudson River, IMC and DRW all employ dozens of FPGA engineers. Verilog/SystemVerilog/Vivado experience is a hiring requirement.

16. C++ template metaprogramming — compile-time exchanges

HFT C++ is very different from ordinary C++: no dynamic allocation, no virtual functions, no std::shared_ptr, no std::function. Instead:

- **CRTP (Curiously Recurring Template Pattern).** Static polymorphism that removes vtable overhead.

- **Compile-time dispatch.** `if constexpr` branches with no runtime cost.

- **EBO (Empty Base Optimization).** Empty policy types via inheritance with no memory footprint.

- **PGO (Profile-Guided Optimization)** + LTO + cache-line alignment.

template <typename Policy>

class OrderRouter : public Policy {

public:

void submit(const Order& o) {

if constexpr (Policy::has_pre_risk_check) {

Policy::pre_risk(o);

}

Policy::route(o);

}

};

struct CmeFixedRiskPolicy {

static constexpr bool has_pre_risk_check = true;

static void pre_risk(const Order&) { /* fixed risk */ }

static void route(const Order& o) { /* fast path */ }

};

OrderRouter<CmeFixedRiskPolicy> cme_router;

Most firms maintain their own standard library — allocator-free vectors, lock-free queues, custom hash maps. Jane Street chose OCaml, but Citadel, Optiver, Hudson River and IMC are C++-centric.

17. kdb+/q — the time-series standard

[kdb+](https://kx.com/) is a columnar in-memory database designed by Arthur Whitney in 1993, with a functional query language q (descendant of APL/K). Single-liners are dense — alien at first, but the de facto standard for time-series.

/ KS200 futures 1-second bars for today

trades: select last px, sum sz by 1 xbar time.second

from trades where sym=`KS200, date=.z.d

/ 30-bar moving average and stdev

mavg30: 30 mavg trades.px

mdev30: 30 mdev trades.px

/ Upper Bollinger breakout

breakout: select from trades where px > mavg30 + 2 * mdev30

/ Per-minute volatility

vol_per_min: select sdev px by 1 xbar time.minute from trades

kdb+ processes billions of rows per second on a single node and unfolds columns in memory to use SIMD. Its licensing is notoriously expensive, so open-source rivals (QuestDB, ClickHouse, Druid) keep encroaching — but the conciseness of kdb+ stat-arb code remains hard to match.

18. Real-time risk — VaR, position limits, kill switch

Trading proprietary capital, risk management is existential. Core tools.

- **Real-time VaR.** Revalues all positions every second and compares against 95% / 99% VaR limits. Auto-liquidates on breach.

- **Greeks limits.** Options desks have separate Delta, Gamma, Vega limits.

- **Per-symbol position limits.** Exchange gateways block excessive single-name exposure.

- **Fat-finger check.** Orders 10× normal size are auto-rejected.

- **Kill switch.** A one-command stop for the firm's order flow. Post-Dodd-Frank, effectively mandatory.

Knight Capital's `$440M` loss in 2012 is the cautionary tale — a botched deploy unleashed 45 minutes of bad orders and effectively destroyed the firm. Since then, every shop runs multi-layer kill switches and canary rollouts.

19. Reg NMS and MiFID II SI — US and EU regulation

**Reg NMS (Regulation National Market System).** Introduced by the SEC in 2007. Key provisions:

- **Rule 611 (Order Protection Rule).** Exchanges must not trade through the National Best Bid and Offer.

- **Rule 610 (Access Rule).** Standardized access fees across exchanges.

- **Rule 612 (Sub-Penny Rule).** No sub-`$0.01` quotations for stocks priced ≥ `$1`.

Reg NMS effectively fragmented US equities into 13 exchanges and 30+ ATSes (dark pools). The market makers that stitch those fragments together are the HFT firms.

**MiFID II SI (Systematic Internaliser).** Introduced in the EU in 2018. Firms that internalize customer orders against their own capital must register as SIs and publish quotes / report executions. Citadel Securities Europe, Virtu Financial Ireland and Optiver SI are all registered.

The SEC's 2024 **Order Competition Rule** proposal sought to mandate auctions for retail order flow but was shelved again in 2025. The tug-of-war over PFOF continues.

20. KRX algorithmic-trading pre-registration — Korea's regulation

The [Korea Exchange (KRX)](https://www.krx.co.kr/) introduced algorithmic-trading pre-registration in 2014. Key points.

- **Mandatory registration.** Algo ID, strategy type and daily average order volume must be filed with KRX.

- **Quote-to-fill ratio.** Below a threshold and the firm pays surcharge fees.

- **Volatility halt.** Auto-halts when market volatility breaches a threshold (circuit breakers).

- **Foreign market-maker obligations.** Registered foreign market makers must maintain a minimum quoting ratio.

In 2026, KRX-registered foreign market makers include Optiver, IMC, Tower Research, Citadel Securities Korea (Seoul office) and DRW. Domestically, the algo desks at NH Investment & Securities, Mirae Asset, Kiwoom, Korea Investment & Securities and KB Securities act as market makers (MMs).

21. Korea HFT — NH Investment & Securities, Mirae Asset, Kiwoom

In Korea, "HFT" usually refers to foreign firms — but domestic securities firms running proprietary algorithmic trading are functionally HFT too.

- **NH Investment & Securities Algorithmic Trading.** Major market maker in KOSPI 200 futures and options. The #1 domestic ETF LP by activity in 2024. C++ / kdb+ stack.

- **Mirae Asset Securities Auto-Trading Team.** Most active among KOSDAQ market makers. Runs proprietary arbitrage and ETF AP. Chairman Park Hyun-joo personally backed systematic trading.

- **Kiwoom Securities.** Dominant retail HTS broker, with a proprietary arbitrage desk on top. Yeongwoongmun API plus in-house algorithms.

- **Korea Investment & Securities.** Global rates plus KRX bond market making.

- **KB Securities.** ELS hedge-book auto-hedging that is effectively options HFT.

After the 2023 SG-related CFD incident, KRX tightened algo-trading monitoring. From 2025, exchange gateways enforce fat-finger blocks.

22. Japan HFT — Nomura, MUFG, SBI, Daiwa

Japan's algo-trading market opened later than the US but exploded after the Tokyo Stock Exchange rolled out arrowhead in 2010.

- **Nomura Algorithmic Trading.** US market making via Instinet plus a domestic Japan desk. Options market maker.

- **Mitsubishi UFJ Morgan Stanley (MUMSS).** JGB and TOPIX futures market maker.

- **SBI Holdings HFT desk.** FX HFT via SBI Liquidity Market, with lines from Tokyo to Southeast Asia and the Middle East.

- **Daiwa Securities algo.** Japanese equity algorithms plus bond market making.

- **Foreign firms.** Optiver, IMC, Citadel Securities and Jump Trading run Tokyo offices, all appearing as foreign market makers on OSE Nikkei 225 options.

After the Bank of Japan exited negative rates in 2024, algorithmic activity in JGBs jumped; MUFG and Daiwa more than doubled the size of their algo books.

23. ETP (Exchange Trade Pad) — Jane Street's workstation

[Jane Street ETP](https://www.janestreet.com/tech-talks/) is the firm's proprietary trading workstation. Written in OCaml, it sits on virtually every trader's desk in place of a Bloomberg terminal. Public material is scarce, but conference talks have revealed pieces.

- **Single codebase.** ETP, the risk engine, the simulator and the option pricing library all share the same OCaml code.

- **Visualization.** ETP renders grids, charts and order tickets via a React-equivalent OCaml UI library.

- **Backtesting.** The same code runs live and in the simulator with the same semantics.

ETP's design philosophy: the distance between trader and engineer is zero. Most Jane Street traders can write code and build signal widgets directly on top of ETP.

24. 2026 outlook — AI, quantum, and the regulators

**AI signals everywhere.** Through 2024–2025, Two Sigma, Citadel and Jane Street all rolled transformer-based signal models into production. These are domain-specific models — not generic chatbots — that fuse tick embeddings with news and order-flow embeddings, and reportedly add 0.5–1bp of alpha on short horizons.

**Quantum's promise vs the limit.** Goldman Sachs with D-Wave and IBM Q claimed quantum advantage in option pricing and portfolio optimization, but in 2026 the industry standard is still classical Monte Carlo plus GPU. Quantum becoming meaningful in option HFT is more plausibly a post-2030 story.

**Regulation — SEC vs EU seesaw.** The US debate over PFOF, information flow, co-lo fairness and market-data fees rolls on; the EU's third MiFIR revision tightens capital requirements on algorithmic trading. KRX plans to roll out its next-generation system in 2027, and JPX is launching arrowhead 4.0 in 2026.

**End of cross-asset boundaries.** HFT that began in US equities, options, futures and bonds now stretches into crypto (Jump Crypto, Cumberland/DRW, Jane Street Crypto), carbon credits, JGBs, India's NSE, Vietnam's HOSE. Most observers see tokenized US Treasuries and tokenized real estate as the next venues.

25. References

- Citadel Securities: https://www.citadelsecurities.com/

- Jane Street: https://www.janestreet.com/

- Jane Street Tech Talks: https://www.janestreet.com/tech-talks/

- Two Sigma: https://www.twosigma.com/

- Optiver: https://optiver.com/

- Jump Trading: https://www.jumptrading.com/

- Virtu Financial: https://www.virtu.com/

- IMC Trading: https://www.imc.com/

- Tower Research Capital: https://www.tower-research.com/

- Hudson River Trading: https://www.hudsonrivertrading.com/

- Flow Traders: https://www.flowtraders.com/

- DRW: https://drw.com/

- SEC Regulation NMS: https://www.sec.gov/rules/final/2005/34-51808.pdf

- ESMA MiFID II / MiFIR: https://www.esma.europa.eu/policy-rules/mifid-ii-and-mifir

- Korea Exchange (KRX) algorithmic trading: https://www.krx.co.kr/

- Japan Exchange Group (JPX) arrowhead: https://www.jpx.co.jp/english/equities/trading/domestic/index.html

- kdb+ / KX Systems: https://kx.com/

- AMD Xilinx FPGAs: https://www.amd.com/en/products/adaptive-socs-and-fpgas.html

- Solarflare Onload (Xilinx): https://www.xilinx.com/products/boards-and-kits/x2-series.html

- *Flash Boys* by Michael Lewis (2014): https://wwnorton.com/books/Flash-Boys/

- "Trading and Exchanges" by Larry Harris (2003)

- CME Globex MDP 3.0: https://www.cmegroup.com/confluence/display/EPICSANDBOX/MDP+3.0

- Nasdaq TotalView-ITCH: https://www.nasdaqtrader.com/Trader.aspx?id=ITCH

- NYSE Pillar: https://www.nyse.com/markets/nyse-pillar

- Jane Street OCaml Library (Core): https://github.com/janestreet/core