Quick glimpse of market microstructure of electronic limit order - - PowerPoint PPT Presentation

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Quick glimpse of market microstructure of electronic limit order book markets

Costis Maglaras

Columbia Business School

Oct 2020

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Specifically... interplay between algorithmic trading & LOBs

◮ equities execution ecosystem & algorithmic trading ◮ the financial exchange as a limit order book ◮ prototypical problems in trade execution that involve queueing / LOB dynamics: – order placement . . . , estimation of expected delay to fill order – adverse selection – order routing – optimal execution in LOB and short-term impact costs ◮ descriptive analysis of LOB dynamics (e.g., inter-temporal price dynamics, short-term volatility) ◮ trading signals ◮ market design, regulation & trading implications

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Simplified view of US equities trading

portfolio manager (buy-side) algorithmic trading engine (buy- or sell-side) ? ARCA NASDAQ BATS … Dark Pool #1 … market centers ? market makers / high-frequency traders

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Simplified view of US equities trading - (b)

◮ Electronic ◮ Decentralized/Fragmented NYSE, NASDAQ, ARCA, BATS, Direct Edge, . . . , IEX ◮ Exchanges (∼ 70%) electronic limit order books (LOBs) ◮ Alternative venues (∼ 30%) ECNs, dark pools, internalization, OTC market makers, etc. ◮ Broker dealers: provide information (often not tracked by investors), technology, trading algorithms, market access, liquidity ◮ Market participants increasingly automated – institutional investors: “algorithmic trading” (differ on holding times) – market makers: “high-frequency trading” (∼ 60% ADV) – opportunistic/active & systematic liquidity providers: “aggressive/electronic” – retail: “manual” (∼ 5% ADV; small order sizes)

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Institutional traders (broad strokes)

◮ investment decisions & trade execution are often separate processes ◮ institutional order flow typically has “mandate” to execute ◮ trader selects broker, algorithms, block venue, . . . (algorithm ≈ trading constraints) ◮ main considerations: – “best execution” – access to liquidity (larger orders) – short-term alpha (discretionary investors) – information leakage (large orders the spread over hrs, days, weeks) – commissions (soft dollar agreements) – incentives (portfolio manager & trading desk; buy side & sell side) ◮ execution costs feedback into portfolio selection decisions & fund perf ◮ S&P500: – ADV ≈ <1% MktCap (.1% – 2%) – Depth (displayed, top of book) ≈ .1% ADV – Depth (displayed, top of book) ≈ 10−6 − 10−5 of MktCap ⇒ orders need to be spread out over time

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Market Makers & HFT participants (broad strokes)

◮ supply short-term liquidity; detect flow imbalance and facilitate price discovery; capture bid-ask spread; mostly intraday flow; limited overnight exposure ◮ small order sizes ∼ depth; short trade horizons / holding periods ◮ profit ≈ (captured spread) - (adverse selection) - (TC) – critical to model adverse selection: short term price change conditional on a trade ◮ important to model short term future prices (“alpha”): – microstructure signals (limit order book) – time series modeling of prices (momentum; reversion) – cross-asset signals (statistical arbitrage, ETF against underlying, . . . ) – news (NLP) – detailed microstructure of market mechanisms · · · ◮ risks: adverse price movements; flow toxicity; accumulation of inventory & aggregate market exposure

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Queueing in algorithmic trading and limit order book markets

◮ equities execution ecosystem & algorithmic trading systems ◮ the financial exchange as a limit order book ◮ prototypical problems in LOB that involve queueing considerations: – order placement . . . , estimation of expected delay to fill order – adverse selection – order routing – optimal execution in LOB and short-term impact costs ◮ descriptive analysis of LOB dynamics (e.g., inter-temporal price dynamics, short-term volatility) ◮ trading signals ◮ market design, regulation & trading implications

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Algorithmic Trading Systems: typically decomposed into steps

◮ Forecasts of intraday market variables: volume, spreads, volatility, market depth, . . . ◮ Short-term drift (α) signals: statistical . . . e.g., LOB info to incorporate adverse selection & MM behavior; natural flow imbalance; etc. ◮ Trade scheduling: splits parent order into ∼ 5 min “slices” – relevant time-scale: min-hrs – schedule follows user selected “strategy” (VWAP, POV, IS, . . . ) – reflects investor urgency, “alpha,” risk/return tradeoff – schedule updated during execution to reflect price/liquidity/signals/. . . ◮ Optimal execution of a slice (“micro-trader”): tactically executes slice by further spliting it into child orders – time-scale: sec–min (queue time; short-term LOB dynamics) – optimizes pricing, timing, and management of orders in LOB – execution adapts to short term LOB dynamics, signals, ... ◮ Order routing: decides where to send each child order – relevant time-scale: ∼ .1–100 ms – time/rebate (queueing) tradeoff, liquidity/price, latency, info leakage. . . separation of last two steps mostly technological/historical artifact

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Algorithmic Trading Systems: basic building blocks

◮ forecasts & real-time analytics for intraday trading quantities – volume – volatility – bid-ask spread – market depth – . . . ◮ LOB: – spread dynamics – short-term volatility – signed (buy/sell) volume . . . (not random(?) for short time scales) – effective tick size – cross-asset dependence – short-term impact costs ◮ how we model market participants. . .

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Queueing in algorithmic trading and limit order book markets

◮ equities execution ecosystem & algorithmic trading systems ◮ the financial exchange as a limit order book ◮ prototypical problems in LOB that involve queueing considerations: – order placement . . . , estimation of expected delay to fill order – adverse selection – order routing – optimal execution in LOB and short-term impact costs ◮ descriptive analysis of LOB dynamics (e.g., inter-temporal price dynamics, short-term volatility) ◮ trading signals ◮ market design, regulation & trading implications

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LOB schematic

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The Limit Order Book (LOB)

price ASK BID buy limit order arrivals sell limit order arrivals market sell orders market buy orders cancellations cancellations

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LOB: event driven (short-term) view

price pN λb

N

λs

N

· · · · · · pat +1 λs

at +1

pat λs

at

· · · pbt λb

bt

pbt −1 λb

bt −1

· · · · · · p1 λb

1

buy limit order arrival rates sell limit order arrival rates µs

bt

sell market order rate µb

at

buy market order rate γ cancellation rate γ cancellation rate

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LOB re-drawn as a multi-class queueing network

µs

bt

market sell

• rders

λb

bt , γ

. . . . . . λb

1, γ

limit buy orders µb

at

market buy

• rders

. . . λs

at , γ

. . . λs

N, γ

limit sell orders

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Multiple Limit Order Books

exchange 1 exchange 2 . . . exchange N national best bid/ask (NBBO)

Price levels are coupled through protection mechanisms (Reg NMS)

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Execution in LOB: key modeling and trading decisions

◮ real-time measurements and forecasts for event rates (arrivals, trades, cancellations on each side of the LOB) ◮ heterogenous limit order, cancellation & trade flows ◮ time/price queue priority: – estimate queueing delay & P(fill in T time units) – limit order placement . . . depends on queueing effects at each exchange – maintain / estimate queue position (& residual queueing delay) – adverse selection as a fcn of exchange, depth, queue position, . . . – opportunity cost (book moves/jump away) as fcn of depth, time-to-go, – transaction cost models (Processor Sharing in some (very) liquid futures instr.) ◮ microstructure, short-term alpha signals ◮ optimize execution price by tactically controlling – when to post limit orders, and to which exchanges – when to cancel orders – when & how to execute using market orders – typical control problem horizon ∼ queue time-to-fill

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Key points . . .

◮ queueing is an important phenomenon in electronic LOB markets ◮ in the context of electronic trading, queueing delays – introduce risk or market exposure – dictate order routing in fragmented markets – shape MM liquidity provision trading strategies – create incentives for competition among MM and among exchanges – affect magnitude and propagation of market impact costs ◮ from stochastic modeling viewpoint LOBs introduce new/novel stochastic modeling, control and perf analysis questions – coupling – heterogenous flows/participants (a variation on “multi-class”) – should we model rate functions or strategy interaction? ◮ insight on market design & regulation, e.g., – should exchanges charge/pay same fees? lower/higher fees? – time/price versus PS/price – trade/cancel throttles; transaction tax; internalization; . . .

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Event rates (top of book)

100 200 300 400 500 5 10 15 20 25 30 Arrivals Cancellations Trades ADV rank Event rates (# events/sec)

Figure

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Normalized event rates (top of book)

100 200 300 400 500 5 10 15 20 Arrival: λ/µ Cancellations: C/µ ADV rank Normalized event rates

Figure

◮ cancellation volume (at top of book) ≫ trade volume ◮ arrival volume (limit orders at top of book) ≫ traded volume

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Interarrival times (top of book)

100 200 300 400 500 3 6 9 12 15 ADV rank Event inter-arrival times (sec) 100 200 300 400 500 −2.5 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 Arrivals Cancellations Trades ADV rank log (event inter-arrival times (sec))

◮ liquid stocks: # trades, # cancellations, # limit order arrivals are large ◮ # trades ≈ 1 order of magnitude less frequent than cancels or order arrivals

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Heterogeneous event dynamics over 100 microseconds

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Heterogeneous event dynamics over 1 sec

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Variability of order arrival rates

% obs. in ±2σt % obs. in ±3σt % obs. outside ±3σt 1 min 63.33% 79.23% 20.77% 3 min 32.56% 50.39% 49.61% 5 min 27.27% 35.06% 64.94% 10 min 13.16% 31.58% 68.42%

◮ table checks if µt+1 ∈ intervals µt ± kσt for k = 2, 3 ◮ (λ, µ) exhibit significant differences in the time scale of 3 - 5 minutes ◮ cf. top 100 names (by ADV): typical queueing delays = 1 – 100 sec

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Tick period / queueing delay against # trade events

20 40 60 80 100 0.2 0.4 0.6 0.8 1 # trade events per day (1,000’s) Tick period/queueing delay

Figure: Tick period versus queueing delay: ratio against # trade events. (liquid names)

◮ tick period = avg time between changes in the mid-price ◮ tick period is on same (or smaller) order magnitude as queueing delay

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Tick period versus queueing delay: log-log

7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 −3.60 −3.20 −2.80 −2.40 −2.00 −1.60 −1.20 −0.80 −0.40

y = 0.2745x − 3.8102

log (# trade events) log (tick period/queueing delay)

Figure: Tick period versus queueing delay: log-log, slope = 0.27<0.5.

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Tick period versus queueing delay (liquid names): log-log

10 10.5 11 11.5 12 12.5 13 13.5 −3.50 −3.10 −2.70 −2.30 −1.90 −1.50 −1.10 −0.70 −0.30 0.10 0.50

y = 0.1417x − 2.7603

log (# trade events) log (tick period/queueing delay)

Figure: Tick period versus queueing delay: log-log, slope = 0.14<0.5.

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Some observations

◮ Event data: λ ≫ µ and cancellation flow ≫ µ ◮ significant cancellation volume to balance order flow at top of book ◮ price changes on the same time-scale as queueing delays ◮ event rates fluctuate at slightly slower time scale than queueing delays ◮ heterogeneous trading behavior may impact order flow dynamics ◮ fragmentation affects delay estimates and cancellation behavior

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Limit order arrivals

◮ Poisson? ◮ rate fcn’s λ (limit order submissions), µ (trades = service completions) – time-of-day – price level, distance from best bid / best ask, spread – depth, certainly at top of book – effective tick size – rates of other flows; large blocks; . . .

• ther possible considerations:

– model “strategies” that generate flow, e.g.,

• POV responds to (filtered) volume
• HFT participants respond “quickly” to queue depletion events

. . .

structurally estimate state-dependent rate fcn (complex / over fitting? / depends on intended use) ◮ jumps or bursts?

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Trade flows & order sizes

◮ most trades in increments of round lots: 100, 200, . . .

top 500 names (ADV) top 1000 names (ADV) Q1 (# shares) 87 84 Q2 (# shares) 101 101 Q3 (# shares) 151 139

◮ odd lots (mostly < 100 share trades – non-negligible) ◮ roll up prints over δt to account for “simultaneous” trades ◮ think in $ or in shares (or in depth multiples)? ◮ trade sizes are heavy-tailed (lognormal gives reasonable fit) ◮ distinguish trades that happen on exchanges (as opposed to dark pools) µ = µe.d. + µflow and µ = µLOB + µint . . . µLOB = µe.d. + µflow|Q, and µint = µflow| ¯

Q;

µe.d. ∼ 50%µ

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Cancellations

• 1. disregard cancellations
• 2. timer-based cancellations:

– each limit order has associated with it a patience ξ – ξ ∼ exp(γ) ⇒ cancellation outflow ≈ −γQ(t)δt – some general patience distributions also tractable (asymptotically) – state-dependent cancellation flow “stabilizes” queues – reasonable model for child orders generated by some trading algorithms

• 3. constant cancellation outflow ≈ −ηδt

– state independent (not good) – no feedback stabilization, i.e., as Q(t) ↑ cancellation flow constant – but, more tractable

• 4. event-driven. . . MM behavior

C = Ce.d. + Ct where Ce.d. ∼ 75%C

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Heterogenous trading behaviors

◮ different market participants exhibit significantly different behavior wrt – limit order submission – cancellations – trade sizes & trade submission triggers ◮ should we model flow through one order generating process? (single type model) – e.g., Poisson (λ(t, state vars)), sizes ∼ G, patience ∼ F ◮ or model heterogenous behavior and use a mixture model, e.g., – algo: Poisson (λ(t, state vars)), sizes ∼ Geo(1/s), patience ∼ exp(θ) – MM: event driven arrivals, cancels, trades (fcn of state and signals) – blocks: Poisson(η(t, state vars)), sizes ∼ lognormal

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Queueing in algorithmic trading and limit order book markets

◮ equities execution ecosystem & algorithmic trading systems ◮ the financial exchange as a limit order book ◮ prototypical problems in LOB that involve queueing considerations: – order placement . . . , estimation of expected delay to fill order – adverse selection – order routing – optimal execution in LOB and short-term impact costs ◮ descriptive analysis of LOB dynamics (e.g., inter-temporal price dynamics, short-term volatility) ◮ trading signals ◮ market design, regulation & trading implications

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LOB: event driven (short-term) view

price pN λb

N

λs

N

· · · · · · pat +1 λs

at +1

pat λs

at

· · · pbt λb

bt

pbt −1 λb

bt −1

· · · · · · p1 λb

1

buy limit order arrival rates sell limit order arrival rates µs

bt

sell market order rate µb

at

buy market order rate γ cancellation rate γ cancellation rate

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Stylized optimal execution in a LOB

• bjective: how to buy C shares within time T at the lowest price

controls: how much, when, at what prices to trade ◮ trade with limit orders / market orders ◮ trade with block trades / continuously submitted trades (rate upper bounded by κi) – T is same order of magnitude as the queueing delays (≈ 1 - 5 min) – microstructure of the LOB affects execution policy and resulting costs – simple motivating problem generates insight on execution strategies . . . and impact cost drivers

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Motivating questions

◮ how long does it take until a limit order gets filled? ◮ risk that a large block or informational event arrives during that time? (adverse selection & opportunity cost) ◮ how do different market participants trade in the LOB? (incentives) ◮ equilibrium behavior of LOB dynamics ◮ tactical execution in a LOB ◮ steady state properties of the market: spread, volatility, depth ◮ how does mkt structure (regulations) affect mkt equilibrium?

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Limit order placement, and queueing delays

◮ estimation of expected delay until a limit order gets filled ◮ related questions: – estimate queue position while in queue – estimate residual delay until an order gets filled while in queue – relevant in deciding when to place limit orders taking into account scheduling objective – routing of orders across exchanges (that may differ in their expected delays) – input to understanding adverse selection

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Two different estimates of delay (liquid, deep queue (λ ≫ µ)) – 1

λ µ γq(t)

◮ Naive estimate (no cancellations, γ = 0): w 0 = q(0) µ

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Two different estimates of delay (liquid, deep queue (λ ≫ µ)) – 2

λ µ γq(t)

◮ Naive estimate (no cancellations, γ = 0): w 0 = q(0) µ ◮ Proportional cancellations: w 1 = 1 γ log

• 1 + q(0)γ

µ

• derivation of w 1 uses fluid model of M/M/1 + M:

w 1 = inf{t ≥ 0 : q(t) = 0} ODE: ˙ q(t) = −µ − γq(t) ⇒ q(t) = −µ γ

• 1 − e−γt

+ q(0)e−γt

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Queue position as fcn of sojourn time s

x(s) = queue position s time units after posting infinitesimal (patient) order ◮ No cancellations: q(s) = q(0) − µs – linear progress through the queue ◮ Proportional cancellations (exp. patience): x(s) = q(0) − λ

s

e−γtdt =

• q(0) − λ

γ

• + λ

γ e−γs – non-linear movement thru queue; impatient traders cancel early

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Residual delay as fcn of queue position at time s

x(s) = queue position s time units after posting infinitesimal (patient) order ◮ No cancellations: w 1(x(s)) = x(s) µ , x(0) = q(0) ◮ Proportional cancellations (exp. patience): w 2(x(s)) = 1 γ log

• 1 + x(s)γ

µ

• x(0) = q(0)

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Realized delays vs. estimates

◮ dataset: 325,000 algo limit orders, Mar-Apr 2012, ≈500 symbols ◮ fields: date, time (ms), exchange, symbol, buy/sell, parent strategy (e.g., VWAP), outcome, waiting time (till execution or cancellation) ◮ we estimated model parameters using trailing 3 minute statistics (TAQ) ◮ filtered symbols with too few points, to end with 109,000 orders, 268 symbols ◮ uncensored delay observations (the data set was censored due to cancels (65% of orders)

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Realized delays vs. estimates (sample: 325,000 algo orders Mar-Apr 2012)

Figure: Realized limit order delays Du (x axis) compared to delay estimates with proportional

cancelations (blue), or no cancelations (red). Realized delays uncensored (max entropy).

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Treatment of cancellations seems relevant to accuracy of delay estimates ◮ ∼ 80% of orders get cancelled ◮ disregarding cancellations seems too drastic of a simplification ◮ exponential patience / proportional cancellations appear too optimistic

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Alternate model: constant (state-independent) cancellation intensity

˙ q(t) = λ − µ − η, 0 > η ≥ λ − µ ◮ v(s) = µ + (x(s)/q(0))η = speed of moving through queue after s time x(s) = q(0) −

s

v(t)dt = q(0) − µs −

s

(η/q(0))x(t)dt ⇒ ˙ x(s) = −µ − (η/q(0))x(s) It follows that w 2 = inf{t ≥ 0 : x(t) = 0} = · · · = q(0) η log

λ

µ

• ◮ If queue is stable, then η ≥ λ − µ. Set η = λ − µ.

M/M/1 + M: equilibrium depth q∞ s.t. λ = µ + γq∞ ⇒ η = γq∞. if q(0) = q∞, w 1 = 1 γ log

• 1 + γq(0)

µ

• = q(0)

η log

λ

µ

• = w 2

if q(0) < q∞, then w 2(q(0)) < w 1(q(0)) (and vice versa)

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need more nuanced model to estimate cancellation effect on delay

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Cancelations depend on LOB state

Figure: State-dependent cancelations - more orders cancel from small queues. (grey:

(cancellations in δt intervals) (in shares); red: (cancellations in δt)/Qt ) ◮ exp. patience ⇒ proportional cancellation model ≈ γQtδt ⇒ (cancellations in δt)/Qt ≈ γ (i.e., constant) ◮ data shows normalized cancellation intensity ր as normalized queue size ↓

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Bursty event behavior & cancellation mechanism

Observations: ◮ Event rates increase when queues are small (and likely to get depleted) ◮ Cancellations increase when queues are small

– why? – does it matter in estimating delays and in order placement?

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Limit order FIFO queue with two types of order flow

◮ Type-1 orders (algorithmic flow):

◮ Arrive (join the queue) according to a Poisson process with rate λ ◮ Cancel according to finite deadlines ∼ exp(γ)

◮ Type-2 orders (MM) - event driven:

◮ Join right after any other order joins, with probability F, as long as the queue length q(t) > θ ◮ Cancel all orders immediately whenever q(t) ≤ θ – for simplicity assume that θ is common across all type 2 orders

◮ Market orders arrive according to a Poisson process with rate µ. ◮ Intuition:

– when q(t) is small, a cascade of type-2 order cancelations is likely – when q(t) is large, type-2 orders increase depth and waiting times (“order crowding”)

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Associated fluid model

λ · f 1{q(t)>δ} λ µ γq1(t)

◮ qi(t) = type i orders, i = 1, 2 ◮ q(t) = q1(t) + q2(t) = total queue content ◮ cancellation behavior: – type 1: −γq1(t) ⇐ ξ ∼ exp(γ) – type 2: all q2(t) cancels if q(t) ≤ θ ◮ α(t) = % of µ that trades with type 1

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Contrasting delay estimates against realized delays

Figure: Waiting times with one-type model w1, with no cancelations w0, with two-type model w compared to realized delays Du.

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Rough intuition

◮ need to estimate mixture of patient vs. inpatient orders ◮ incorporate “crowding” out effect of patient orders ◮ resulting delay estimate is not as pessimistic as q/µ (no cancellations) ◮ fragmentation . . . need delay estimates for each exchange ◮ internalization. . . estimate conditional volume that hits exchange (i.e., not internalized) SO WHAT?

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Flow heterogeneity has 1st order effect on LOB behavior

◮ Adverse selection and opportunity costs ◮ Heterogenous trading behavior should affect execution in – order placement – cancellations – market orders ◮ possible explanation for anomalously long waiting times in large queues despite large cancellation rates (some orders never cancel, and in long queues only these orders survive) ◮ significant differences on state-dependent behavior across types of flow – MMs flow sensitive to AS costs, primarily state-dependent policies – algo flow driven by strategy participation considerations, mostly “timer-based” Possible approaches: – work with state- & price-dependent event rates – self-exciting process models – model trading behaviors (game?)

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Recap - 1

◮ modeling strategic cancellations is important ◮ trader behavior is heterogeneous (aka. trading strategies) ◮ important to model network effects . . . state dependent actions depend on other queues, events, exogenous market info, other securities

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Followup question. . .

◮ probability that an order will get filled ◮ conditional probability that this will be an “adverse” fill ◮ estimate adverse selection costs as a fcn of queue position

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Queueing in algorithmic trading and limit order book markets

◮ equities execution ecosystem & algorithmic trading systems ◮ the financial exchange as a limit order book ◮ prototypical problems in LOB that involve queueing considerations: – order placement . . . , estimation of expected delay to fill order – adverse selection – order routing – optimal execution in LOB and short-term impact costs ◮ descriptive analysis of LOB dynamics (e.g., inter-temporal price dynamics, short-term volatility) ◮ trading signals ◮ market design, regulation & trading implications

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Adverse selection

The issue: ◮ for a limit order to get filled, a trader must decide to cross the spread ◮ that action may convey information about the price (that may move adversely) ◮ more likely to get filled by a large trade if at the back of the queue ◮ large trades often indicate future price movements The role of queue position: – front of queue . . . less waiting time, higher probability of a fill, could trade against small counter order – back of queue . . . higher waiting time, smaller probability of a fill, likely to trade against a large (informed) trade . . . higher probability that you may regret trading at that price

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Simple schematic to aid adverse selection discussion

◮ what information should we monitor? ◮ which events should we be concerned about?

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Simplified model of price changes – (1)

• i. stochastic fluctuations in queue lengths that lead to occasional queue

depletions – when queue is depleted, with probability 1 − α is bounces back up, and – with probability α the price changes (α ≥ .75)

• ii. flow imbalance “detected” by MM

– MMs maintain noisy estimate of buy/sell imbalance – MMs cancel and/or trade aggressively when imbalance is significant – MMs cancel to avoid AS by filling orders prior to a price change – typically 1-2 ticks and do not require lots of volume to trade

• iii. block trades (informed investors)

– price change as a result of a block of volume traded may be larger

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Simplified model of price changes – (2)

• i. stochastic fluctuations in queue lengths that lead to occasional queue

depletions – when queue is depleted, with probability 1 − α is bounces back up, and – with probability α the price changes

◮ unlikely in liquid & deep securities – λ, µ imbalance is O(n), – queues are O(n) but stochastic fluctuations are O(√n) ◮ disregard this effect in the sequel

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Simplified model of price changes – (3)

• ii. flow imbalance “detected” by MM

– Poisson with rates κ+

1 and κ− 1

– rates could be state dependent (not here; all mkt participants can be tracking)

• iii. block trades (informed investors)

– Poisson with rates κ+

2 and κ− 2

– rates may be price sensitive (e.g., relative to open price, prev close, . . . ) So: – study superposition of Poisson flows – if we model magnitude of price change, we get compound Poisson’s – could also model size (in # shares) of block trades, get compound Poisson

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Setup for adverse selection calculation

◮ given queue position x, d = E(W (x)) = expected delay until the xth order in queue will get filled ◮ events to keep track (convention: +ve jump pushes price away (no fill)): P(fill) = P(no jumps in [0, d] or 1st jump occurs in [0, d] and is -ve) P(fill & not AS) = P(no jumps in [0, d]) P(fill & AS) = P(1st jump occurs in [0, d] and is -ve) P(no fill) = P(1st jump occurs in [0, d] and is +ve) above calculations depend on queue position x through d = E(W (x))

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Probability of an adverse fill

◮ probability of a fill: P(fill) = κ− κ + κ+ κ e−dκ ◮ probability of an adverse fill (due to a jump): P(fill & AS) = (1 − e−dκ)κ− κ and P(fill & AS|fill) = κ−(1 − e−dκ) κ− + κ+e−dκ ◮ probability of non-adverse fill: P(fill & not AS) = P(no jump in [0, d]) = e−dκ ◮ probability of no fill: P(no fill) = (1 − e−dκ)κ+ κ ◮ above consider a “race” between +ve and -ve jumps over the duration d

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Adverse selection of limit orders

P(fill) = κ− κ + κ+ κ e−dκ and P(no fill) = (1 − e−dκ)κ+ κ P(fill & AS) = (1 − e−dκ)κ− κ and P(fill & not AS) = e−dκ – how do we estimate κi’s? – which of these parameters are “observable” in real-time? – AS often measures price moves within ∆t after fill

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Including trading volume considerations & fragmentation

◮ fragmentation: – queue position: order exchanges by fee (lowest to largest) – cheaper exchanges placed ahead; more expensive placed behind – Qfr = depth in front of order; Qbeh = depth behind order – Qoth is the depth on the other side of the book ◮ consider jump size distribution: – Fill: no jump in [0, d] or (-ve) jump of size ≥ Qfr – AS: (-ve) jump of size ≥ Qfr + Qbeh – No Fill: (+ve) jump of size Qoth ◮ intuitive results: – side of next price move depends on relative sizes of bid and ask queues – duration of race depends on d, a function of our queue position – AS ↓ as Qfr ↓ and as Qbeh ↑ – “ubiquitous” queue imbalance seems to emerge

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Recap - 2

◮ time-in-queue, queue position, other queues affect heterogenous order placement/cancellation behavior ◮ queue position affects adverse selection . . . speed race ◮ fees/rebates at different exchanges affect interplay of econ incentives and trading decisions

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Queueing in algorithmic trading and limit order book markets

◮ equities execution ecosystem & algorithmic trading systems ◮ the financial exchange as a limit order book ◮ prototypical problems in LOB that involve queueing considerations: – order placement . . . , estimation of expected delay to fill order – adverse selection – order routing – optimal execution in LOB and short-term impact costs ◮ descriptive analysis of LOB dynamics (e.g., inter-temporal price dynamics, short-term volatility) ◮ trading signals ◮ market design, regulation & trading implications

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Multiple Limit Order Books

exchange 1 exchange 2 . . . exchange N national best bid/ask (NBBO)

Price levels are coupled through protection mechanisms (Reg NMS)

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Time Scales

Three relevant time scales: ◮ Events: order / trade / cancellation interarrival times (∼ ms – sec) ◮ Delays: waiting times at different exchanges (∼ sec – min) ◮ Rates: time-of-day variation of flow characteristics (∼ min – hrs) Order placement decisions depend on queueing delays in LOBs (our focus) ◮ assume constant arrival rates of limit orders and trades ◮ order sizes are small relative to overall flow over relevant time scale ◮ overall limit order and trade volumes are high We will consider a variation of the problem of execution in a LOB that “incorporates” the fragmented nature of markets

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do exchanges differ in their quote size? trading delays?

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DJIA 30: Expected Queue Lengths – Sept 2011

A A A X P B A B A C C A T C S C O C V X D D D I S G E H D H P Q I B M I N T C J N J J P M K F T K O M C D M M M M R K M S F T P F E P G T T R V U T X V Z W M T X O M 101 102 103 104 105

Queue Length (shares, log scale) ARCA NASDAQ BATS EDGX NYSE EDGA

(b) Average queue length (number of shares at the NBBO) across stocks and exchanges.

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DJIA 30: Expected Delays – Sept 2011

A A A X P B A B A C C A T C S C O C V X D D D I S G E H D H P Q I B M I N T C J N J J P M K F T K O M C D M M M M R K M S F T P F E P G T T R V U T X V Z W M T X O M 10−1 100

Expected Delay (minutes, log scale) ARCA NASDAQ BATS EDGX NYSE EDGA

(a) Average expected delay across stocks and exchanges.

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Simplified view via a One-sided Multi LOB Model

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Simple formulation of order routing in fragmented market – (1)

Fragmented exchanges differ wrt ◮ Expected delay (≈ 1 to 1000 seconds), P(fill in t time) ◮ Rebates/fees for limit/mkt orders (≈ −$0.0002 to $0.0030 per share) ◮ . . . order types, latency, tiering agreements with exchanges, . . . max

Xk

• k

(s/2 + rk)XkP(τ f

k < {τ −, τ +, T})

(good fill) +

• k

(s/2 + rk − πas)XkP(τ − < {τ f

k , τ +, T})

(AS fill) +

• k

(s/2 + fk)XkP(T < {τ f

k , τ −, τ +})

(clean up at far) +

• k

(s/2 + fk + θ)XkP(τ + < {τ f

k , τ −, T})

(clean up at worse) – τ f

k = time-to-fill passively in exch k

– τ +, τ − time until price moves away or in favor (entire mkt) – Xk = quantity to get posted at exchange K (at top of book) – θ = effective tick size (assume only 1 price level is cleared)

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Order routing in fragmented market . . . comments – (2)

Clear shortcomings: ◮ trading algorithms typically do not post all quantity if C is large ◮ allow to post inside the spread. . . easy to incorporate ◮ revise decision with a) time-to-go, b) changes in mkt state ◮ E(τ f

k ) depends on mkt state; same for κ−, κ+

◮ care needed to estimate time-to-fill as fcn of mkt state (esp. inverted) Also, previous expressions can be cumbersome to work with. . . borrow “standard trick” from discrete choice and model RVs as Gumbel (EV-I) and use MNL-like closed form expressions skipping details. . . produces intuitive allocations; queueing delay key driver; tractable; modest estimation needs; robust

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Time vs. money tradeoff

despite its many caveats, formulation captures time vs. money tradeoff ◮ time: trade now with a market order or sooner in a less congested LOB ◮ money: trade in a high rebate exchange and also avoid paying the spread ◮ adverse selection (also favors less congested LOB) ◮ opportunity cost (also favors less congested LOB) ◮ incentives are such that most institutional flow tries to be patient how does this manifest itself in practice?

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State Space Collapse I – PCA output

% of Variance Explained % of Variance Explained One Factor Two Factors One Factor Two Factors Alcoa 80% 88% JPMorgan 90% 94% American Express 78% 88% Kraft 86% 92% Boeing 81% 87% Coca-Cola 87% 93% Bank of America 85% 93% McDonalds 81% 89% Caterpillar 71% 83% 3M 71% 81% Cisco 88% 93% Merck 83% 91% Chevron 78% 87% Microsoft 87% 95% DuPont 86% 92% Pfizer 83% 89% Disney 87% 91% Procter & Gamble 85% 92% General Electric 87% 94% AT&T 82% 89% Home Depot 89% 94% Travelers 80% 88% Hewlett-Packard 87% 92% United Tech 75% 88% IBM 73% 84% Verizon 85% 91% Intel 89% 93% Wal-Mart 89% 93% Johnson & Johnson 87% 91% Exxon Mobil 86% 92%

Table 4: Results of PCA: how much variance in the data can the first two principle components explain

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do traders care about fees/rebates? does it manifest in depth, delay, AS? what if exchanges changed fee/rebates? Nasdaq ran experiment in 2015

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Nasdaq experiment (Q1-Q2 ‘15): 15 stocks, reduce fee from 30 to 5 mils

Stochastic analysis of LOB market used to study policy / regulatory issues

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Recap - 3

◮ time/money are 1st order drivers of routing decisions ◮ service completions are strategic ◮ technological limitations and latency play important role in this area

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Original outline

◮ equities execution ecosystem & algorithmic trading ◮ the financial exchange as a limit order book ◮ prototypical problems in trade execution that involve queueing: – order placement . . . , estimation of expected delay to fill order – adverse selection – order routing – optimal execution in LOB and short-term impact costs ◮ descriptive analysis of LOB dynamics (e.g., inter-temporal price dynamics, short-term volatility) ◮ trading signals ◮ market design, regulation & trading implications

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THANK YOU