Order Types & Mechanics

Question 1

(a) (5 marks)

• Best bid = ₹100.50 (highest buy). Best ask = ₹100.55 (lowest sell). (1)
• Spread = 100.55 − 100.50 = ₹0.05. (1)
• Mid-price = (100.50 + 100.55)/2 = ₹100.525. (1)
• Micro-price formula (size-weighted toward the opposite size): $P_{micro} = \frac{P_{bid}\,Q_{ask} + P_{ask}\,Q_{bid}}{Q_{bid}+Q_{ask}}$ Using top-of-book sizes: $Q_{bid}=200+150=350$ at 100.50 — but strictly top level is best price aggregate. Use best-level sizes $Q_{bid}=350$ (all at 100.50), $Q_{ask}=100$. (1) $P_{micro}=\frac{100.50\times100 + 100.55\times350}{350+100}=\frac{10050+35192.5}{450}=\frac{45242.5}{450}=100.5389$ Micro-price ≈ ₹100.5389 (leans toward ask because bid size dominates → upward pressure). (1)

(Accept best-level bid qty = 350 aggregated, or 200 if only first order counted — state assumption. Full marks if formula + reasoning correct.)

(b) (7 marks)

Market BUY 550 walks the ask side by price-time priority:

• Fill 100 @ 100.55 (level t4). Remaining 450. (1)
• Fill 300 @ 100.60 (level t6). Remaining 150. (1)
• Fill 150 @ 100.65 (level t7, partial; 100 left resting). Remaining 0. (1)

VWAP: (2) $VWAP=\frac{100(100.55)+300(100.60)+150(100.65)}{550}=\frac{10055+30180+15097.5}{550}=\frac{55332.5}{550}=100.6045$ VWAP = ₹100.6045.

Slippage vs best ask at arrival (100.55): (2)

• Per share = 100.6045 − 100.55 = ₹0.0545
• Total = 0.0545 × 550 = ₹30.00 (i.e. 55332.5 − 550×100.55 = 55332.5 − 55302.5 = ₹30.00).

(c) (5 marks)

After (b), ask book: 100.65 has 100 left, then 100.60 & 100.55 exhausted. Wait — 100.55 and 100.60 fully consumed; 100.65 has 250−150=100 remaining. No new asks below 100.65. Marketable limit BUY 400 @ 100.62:

• Best ask now 100.65 > limit 100.62 → not marketable against it. (2)
• So zero fills; the order is not marketable. Unfilled 400 shares rest as a bid at 100.62. (2)
• New best bid = 100.62, new best ask = 100.65. Spread = ₹0.03. (1)

(Key insight: after the market order swept 100.55 and 100.60, the limit at 100.62 cannot reach 100.65, so it rests and improves the bid.)

(d) (5 marks)

Claim: A market order M for quantity Q and a marketable limit order L (same Q, limit L_p ≥ realised worst fill price of M) execute against the same resting liquidity; M's average price ≤ L's is false in general — they are identical or L is weakly worse only by resting. Correct statement:

• Both walk the book from best ask upward (buy). (1)
• Market order fills all Q at successively worse prices; realised worst price = $p^*$. (1)
• Limit order with limit $\ell \ge p^*$ can reach every level M reached, so it fills the same levels for the same quantities → same VWAP. (1)
• If $\ell < p^*$, the limit order stops early, filling fewer shares at better average price but leaving a remainder resting (not fully executed). Thus per-share it is never worse; but it fails the fill-completeness. (1)
• Identical fill condition: $\ell \ge p^*$ and book unchanged between the two arrivals (no intervening orders) ⇒ same fills, same VWAP. (1)

Question 2

(a) (4 marks)

• Upper circuit = 500 × 1.10 = ₹550.00. (1)
• Lower circuit = 500 × 0.90 = ₹450.00. (1)
• GTT sell trigger ₹560 is above the upper circuit (₹550). (1)
• Price cannot trade above ₹550 today ⇒ trigger at 560 can never be hit today ⇒ GTT cannot execute today. (GTT persists to future sessions when band shifts.) (1)

(b) (5 marks)

• Target price = 500 + 15 = ₹515. (1)
• Stop trigger = 500 − 8 = ₹492. (1)
• Stop-market fills at ₹489.30 (gapped/slipped below trigger). P&L = (489.30 − 500) × 100 = −10.70 × 100 = −₹1070. (2)
• Capital deployed = 500 × 100 = ₹50,000. % = −1070/50000 = −2.14%. (1)

(c) (6 marks)

• Slippage = difference between the expected/reference execution price and the actual fill price: $\text{slip} = P_{fill} - P_{ref}$ (signed; adverse for a seller when fill < ref). (2)
• Stop-LIMIT scenario: trigger ₹492 activates a limit sell at ₹491. If price gaps from ₹493 straight to ₹485 (no trades between 491 and 485 at/above 491), the limit at 491 cannot fill because market is now below the limit → order rests unfilled, position stays open. (2)
• If price then falls to ₹470 with the position still open, mark-to-market loss = (470 − 500) × 100 = −₹3000, versus intended stop loss ≈ (492−500)×100 = −₹800. Additional loss = 3000 − 800 = ₹2200 relative to intended protection. (2)

(d) (5 marks)

function simulate_bracket(entry, tp_offset, sl_offset, price_path):
    target = entry + tp_offset        # long: profit above
    stop   = entry - sl_offset        # long: loss below
    for p in price_path:
        if p >= target:               # target checked first
            return (target, "target")   # or p, per fill convention
        if p <= stop:
            return (stop, "stop")
    return (price_path[-1], "open")   # never triggered

Marks: correct target/stop computation (1), loop over ticks (1), target-before-stop ordering (1), stop branch (1), open/return-last fallback (1).

Question 3

(a) (3 marks)

• Objective: choose opening price $P^*$ that maximises total executable (matched) volume; if multiple prices tie on volume, pick the one with minimum imbalance (|cum demand − cum supply|); further ties → price closest to reference. (2)
• Differs from continuous matching because all orders are aggregated and cleared at one single uniform price (uniform-price auction) rather than sequential price-time matching. (1)

(b) (7 marks)

Buyers willing at price P = those with limit ≥ P plus MKT (300). Sellers willing at P = limit ≤ P plus MKT (200).

Buy limits: 201→400, 200→500, 199→600, 198→300. Sell limits: 198→300, 199→500, 200→400, 201→600.

Cumulative demand (buy, ≥P):

• P=201: MKT300 + 400 = 700 (1)
• P=200: 700 + 500 = 1200 (1)
• P=199: 1200 + 600 = 1800 (1)
• P=198: 1800 + 300 = 2100 (0.5)

Cumulative supply (sell, ≤P):

• P=198: MKT200 + 300 = 500 (1)
• P=199: 500 + 500 = 1000 (1)
• P=200: 1000 + 400 = 1400 (1)
• P=201: 1400 + 600 = 2000 (0.5)

(c) (5 marks)

Matched volume at P = min(demand, supply):

• Maximum matched volume = 1200 at P = 200. (3)
• No tie ⇒ equilibrium opening price = ₹200, traded quantity = 1200 shares. (2)

(d) (3 marks)

• All executable orders trade at the uniform price ₹200. (1)
• Unmatched limit orders (demand 1200 vs supply 1400 → 200 sell shares unfilled, and the marginal buy limits below 200) carry into the continuous session and rest in the order book at their limit prices. (1)
• Unmatched market orders are converted to limit orders at the opening price (₹200) for the continuous session (they do not lapse). (1)

[
  {"claim":"Q1b VWAP of market buy 550 = 100.6045","code":"vwap=(100*100.55+300*100.60+150*100.65)/550; result = abs(vwap-100.6045) < 1e-6"},
  {"claim":"Q1b total slippage vs best ask = 30.00","code":"slip=(100*100.55+300*100.60+150*100.65)-550*100.55; result = abs(slip-30.00) < 1e-6"},
  {"claim":"Q2b bracket stop P&L = -1070 and -2.14%","code":"pnl=(489.30-500)*100; pct=pnl/(500*100)*100; result = abs(pnl+1070)<1e-9 and abs(pct+2.14)<1e-2"},
  {"claim":"Q2 circuit limits 550 and 450","code":"result = (500*1.10==550) and (500*0.90==450)"},
  {"claim":"Q3c equilibrium price 200 maximises matched volume 1200","code":"D={198:2100,199:1800,200:1200,201:700}; S={198:500,199:1000,200:1400,201:2000}; matched={p:min(D[p],S[p]) for p in D}; best=max(matched,key=lambda p:matched[p]); result = (best==200) and (matched[200]==1200)"}
]