Order Flow & Tape Reading

Question 1

(a) (5 marks)

• $\Delta_k = \sum_{i\in k} v_i\epsilon_i$ is net aggressive buying minus selling in bar $k$. $C_k=\sum_{j\le k}\Delta_j$ (telescoping running sum). (1)
• Rising price means aggressive buyers pushing $P$ up. Normally rising $P \Rightarrow$ rising $C$ (buyers dominate). (1)
• Divergence: $\frac{dP}{dk}>0$ but $\frac{dC}{dk}\le 0$. Formally sign$(\Delta P)\ne$ sign$(\Delta C)$ over the window. (1)
• Interpretation: price rises despite net selling delta ⇒ a large passive limit seller is absorbing the aggressive buying at the ask; buyers cannot move price efficiently. This is bearish because when buyers exhaust, the resting seller dominates → reversal down. (2)

(b) (7 marks)

$\Delta_k=$ Buy − Sell:

(1 mark per correct $\Delta$/$C$ pairing, ~5)

• Price rises 100.0 → 100.5 (monotone up / flat), while $C_k$ peaks at bar 2 (1000) then falls to −1300. Clear bearish delta divergence. (1)
• Classification: rising price with heavily negative delta = passive buyers/absorbing... precisely: aggressive sellers increasing yet price won't drop → absorption of selling by a passive buyer initially, but bar 5 price stalls (100.5=100.5) with huge negative delta → transitioning to exhaustion of the up-move; net read = bearish absorption at highs. (1)

(c) (6 marks)

Deltas: $[400,600,-300,-800,-1200]$.

• $\mu = \frac{400+600-300-800-1200}{5} = \frac{-1300}{5} = -260$. (2)
• Variance (population): deviations $=[660,860,-40,-540,-940]$, squares $=[435600,739600,1600,291600,883600]$, sum $=2352000$, $/5=470400$, $\sigma=\sqrt{470400}\approx 685.9$. (2)
• Bar-5 delta z-score: $z_5=\frac{-1200-(-260)}{685.9}=\frac{-940}{685.9}\approx -1.371$. (1)
• Price at bar 5 = new high (100.5, matching bar 4's high, ≥ prior). $z_5=-1.37 < -z^* = -1.0$ ⇒ detector FIRES (absorption/bearish flag). (1)

(d) (4 marks)

import numpy as np
def absorption_signal(buy, sell, price, z_star=1.0):
    delta = buy - sell
    C = np.cumsum(delta)
    mu, sd = delta.mean(), delta.std()  # population std
    z = (delta - mu) / sd
    new_high = price >= np.maximum.accumulate(price)
    return new_high & (z < -z_star)

(1 delta/cumsum, 1 z-score, 1 new-high logic, 1 combine)

Question 2

(a) (3 marks) POC = price level with the highest traded volume = 104 (2600). Definition 1 mark, identification 2.

(b) (9 marks)

Total volume $=400+900+1500+2600+1800+700+300 = 8200$. 70% target $=5740$. (1)

Start at POC 104: cum $=2600$ (31.7%). VA $=\{104\}$. (1)

Compare pair rule (one above vs one below current VA edges):

(2 marks for correct comparisons, 2 for cumulative)

• Step 2 crosses 70% → stop. VA levels = {103,104,105}. (1)
• VAH = 105, VAL = 103, POC = 104. (1)

(marks: total 1, start 1, table steps 4, stop logic 1, final answer 2 = 9)

(c) (5 marks)

Greedy adds the larger single adjacent side, but optimal capture for fixed level-count $L$ is the max-sum contiguous window of length $L$ containing POC (or any window).

Counterexample profile (volumes): [10, 1, 100, 1, 10] with POC at index 2 (=100).

• To capture 3 levels greedily from POC: compare left(1) vs right(1) — tie/either, say add left → {1,100}, then next compare left(10) vs right(1) → add left → window {10,1,100}, sum = 111.
• But choosing the 3-level window starting elsewhere, e.g. [100,1,10] = 111 same; however consider [10, 90, 100, 5, 80], POC=100(idx2), pick 3 levels:
  • Greedy: left(90) vs right(5) → add 90 → {90,100}; next left(10) vs right(5) → add 10 → sum 200.
  • Optimal contiguous 3-window: {100,5,80} = 185, or {90,100,5}=195, or {10,90,100}=200. Here greedy = optimal — so refine.
• Cleaner counterexample forcing suboptimality when the algorithm must be contiguous through POC and one side has a "wall then void": [200, 5, 100(POC), 6, 190], capture 3 levels:
  • Greedy: left(5) vs right(6) → right → {100,6}; next left(5) vs right(190) → right → {100,6,190} sum=296.
  • Alternative 3-window through POC {200,5,100} = 305 > 296. Greedy is suboptimal. ∎

(3 marks valid counterexample with correct greedy trace, 2 marks showing better alternative). Full credit for any construction where a large "far" level is blocked behind a small near level.

(d) (3 marks) $O(M)$: POC found in one pass $O(M)$; VA expansion adds ≤ $M-1$ levels, each step is $O(1)$ pointer comparison → total $O(M)$. Justify: constant work per level, each level added once. (3)

Question 3

(a) (4 marks)

• Spoofing: placing large non-bona-fide orders with intent to cancel before execution, to create a false impression of supply/demand and move price/induce others to trade. (1)
• Layering: multiple spoof orders at several price levels on one side to exaggerate depth. (1)
• Signatures: (i) very high cancel-to-fill / order-to-trade ratio; (ii) large size that vanishes as price approaches it / is placed away from touch and pulled; opposite-side execution coincides. (2 signatures, 2 marks)

(b) (4 marks) $R=\frac{\text{cancelled}}{\text{filled}}=\frac{480}{20}=24$. (2)

• Legal/exchange thresholds for order-to-trade or cancel ratios are typically low (e.g. flag when order-to-trade ≫ ~ a few, many venues investigate ratios >~ 20–50). $R=24$ with sub-3-second lifetimes and repetition ⇒ pattern of intent-to-cancel = suspicious spoofing. Argument must cite: high ratio + short lifetime + repetition + one-sided. (2)

(c) (5 marks)

• Iceberg: displayed $q=100$ reloads $n$ times; observed executed volume $=n\cdot q$. Hidden order true size $Q \ge n\cdot q$; best estimate when reloads stop after $n$ full reloads $\hat Q \approx n\cdot q$ (plus final partial). (2)
• Footprint/delta confirmation: repeated prints hitting the ask with the ask reloading = aggressive buyers absorbed by passive... here institution is the passive reloader on ask (distributing) OR aggressive buyer? Convention: reloading ask that keeps getting lifted = passive seller distributing; if prints are buyer-initiated (at ask) and price doesn't rise → absorption by hidden seller ⇒ cumulative delta rises while price flat = bearish. If institution is the aggressor lifting reloaded offers, delta rises with price = accumulation. Must state direction consistent with tape. (2)
• Estimate $Q$: count reloads until display no longer reloads / price breaks; \hat Q = q\cdot(\text{#reloads}). (1)

(d) (5 marks)

def detect_iceberg(trades, book, level, min_reloads=4, window=10):
    # trades: list of (t, side, price, qty)
    # book:   function book(t, price) -> displayed size at level
    reloads = 0
    last_size = book(trades[0].t, level)
    aggressive_volume = 0
    t0 = trades[0].t
    for tr in trades:
        if tr.t - t0 > window:
            break
        if tr.price == level:
            aggressive_volume += tr.qty
            cur = book(tr.t, level)
            # displayed size drops on hit then reloads back up
            if cur >= last_size and last_size < book(tr.t - eps, level):
                reloads += 1
            last_size = cur
    return reloads >= min_reloads and aggressive_volume > 0

Marks: iteration/window 1, reload detection logic 2, threshold flag 1, aggressive-volume confirmation 1.

[
  {"claim":"Bar deltas and cumulative delta correct; C5=-1300",
   "code":"buy=[1200,1500,1100,900,700]; sell=[800,900,1400,1700,1900]; delta=[b-s for b,s in zip(buy,sell)]; C=[]; s=0\nfor d in delta:\n    s+=d; C.append(s)\nresult = (delta==[400,600,-300,-800,-1200]) and (C==[400,1000,700,-100,-1300])"},
  {"claim":"mu=-260 and bar5 z-score approx -1.371, detector fires at z*=1.0",
   "code":"import statistics as st\ndelta=[400,600,-300,-800,-1200]; mu=sum(delta)/5\nsd=(sum((d-mu)**2 for d in delta)/5)**0.5\nz5=(delta[-1]-mu)/sd\nresult = abs(mu-(-260))<1e-9 and abs(z5-(-1.371))<0.01 and z5 < -1.0"},
  {"claim":"Volume profile POC=104, total=8200, VA {103,104,105} crosses 70% at 71.95%",
   "code":"prices=[101,102,103,104,105,106,107]; vol=[400,900,1500,2600,1800,700,300]\ntotal=sum(vol); poc_i=vol.index(max(vol)); cum=vol[poc_i]\nlo=poc_i; hi=poc_i; steps=[]\nwhile cum/total < 0.70:\n    above = vol[hi+1] if hi+1<len(vol) else -1\n    below = vol[lo-1] if lo-1>=0 else -1\n    if above>=below: hi+