σμimplied vol · KKmax(S−K,0)udβρᵢⱼfat tailsPnL · drawdownyield · TdSₜ = μSₜ dt + σSₜ dWₜC = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)σₚ² = wᵀΣwd₁ = [ln(S/K) + (r + σ²⁄2)T] ⁄ σ√T∂V/∂t + ½σ²S²·∂²V/∂S² + rS·∂V/∂S − rV = 0Sharpe = (Rₚ − R_f) ⁄ σₚVaR₉₉ = μ − 2.33σρ = Cov(X,Y) ⁄ σₓσᵧE[Rₚ] = Σ wᵢ·E[Rᵢ]φ(x) = e^(−x²/2) ⁄ √2πE[Rᵢ] = R_f + βᵢ(E[Rₘ] − R_f)dXₜ = θ(μ − Xₜ)dt + σ dWₜσ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁C − P = S − K·e⁻ʳᵀΔ = ∂V/∂S Γ = ∂²V/∂S²p = (e^(rΔt) − d) ⁄ (u − d)rₜ = ln(Pₜ ⁄ Pₜ₋₁)E[Xₜ₊₁ | ℱₜ] = Xₜf* = (bp − q) ⁄ bz = (x − μ) ⁄ σP(N=k) = λᵏe^(−λ) ⁄ k!Θ = −∂V/∂Tν = S·φ(d₁)·√Tmin wᵀΣw s.t. wᵀμ = μ*∫Σ∂∞λ
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σμimplied vol · KKmax(S−K,0)udβρᵢⱼfat tailsPnL · drawdownyield · TdSₜ = μSₜ dt + σSₜ dWₜC = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)σₚ² = wᵀΣwd₁ = [ln(S/K) + (r + σ²⁄2)T] ⁄ σ√T∂V/∂t + ½σ²S²·∂²V/∂S² + rS·∂V/∂S − rV = 0Sharpe = (Rₚ − R_f) ⁄ σₚVaR₉₉ = μ − 2.33σρ = Cov(X,Y) ⁄ σₓσᵧE[Rₚ] = Σ wᵢ·E[Rᵢ]φ(x) = e^(−x²/2) ⁄ √2πE[Rᵢ] = R_f + βᵢ(E[Rₘ] − R_f)dXₜ = θ(μ − Xₜ)dt + σ dWₜσ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁C − P = S − K·e⁻ʳᵀΔ = ∂V/∂S Γ = ∂²V/∂S²p = (e^(rΔt) − d) ⁄ (u − d)rₜ = ln(Pₜ ⁄ Pₜ₋₁)E[Xₜ₊₁ | ℱₜ] = Xₜf* = (bp − q) ⁄ bz = (x − μ) ⁄ σP(N=k) = λᵏe^(−λ) ⁄ k!Θ = −∂V/∂Tν = S·φ(d₁)·√Tmin wᵀΣw s.t. wᵀμ = μ*∫Σ∂∞λ
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Market Structure skill›Module 3 · After the trade and who trades›Topic 3.2·~40 minBeginner

Market makers and HFT firms

Skill positionModule 3 of 4 · Topic 2 of 2
3.2 Market makers and HFT firms
—Lab score— / 100Total XP—Streak—

Who provides liquidity

A market maker continuously quotes a price to buy (the bid) and a price to sell (the ask) in the same instrument. When other traders hit those quotes, the market maker earns the spread between them. In return it takes on inventory risk: after buying, it holds shares that may fall in value before it can sell them. Some exchanges give designated market makers duties, such as quoting close to the best price, in exchange for fee benefits.

High-frequency trading (HFT) is a style, not a single strategy. HFT firms use very fast systems to send huge numbers of orders, hold positions for seconds or less, earn a tiny profit per trade and usually end the day flat. Many are market makers; others do arbitrage between venues or between an ETF and its components.

Most of the volume that moves prices comes from institutions: pension and mutual funds with large, long-horizon orders that are sliced into small pieces over hours or days, hedge funds with shorter views, and retail investors with small orders that usually reach a wholesaler through their broker.

  • Market maker: quotes both sides, earns the spread, carries inventory risk.
  • HFT firm: very fast, many orders, tiny profit per trade, usually flat overnight.
  • Institution: large orders, long horizon, slices orders over time.
  • Adverse selection: the risk of trading against someone who knows more.
A market maker's spread incomeA market maker quotes 20.00 bid and 20.02 ask. In one day it buys 10,000 shares at 20.00 and sells 10,000 at 20.02. The gross spread capture is 10,000 × (20.02 − 20.00) = 200 USD. If the price drifts down 0.05 while it holds 10,000 shares of inventory, the loss is 500 USD: inventory risk can swamp the spread.
Fast does not mean it sees the futureHFT firms are quick, but their edge is small and comes from lower costs, better queue position and faster reaction to public information, not from knowing what institutions will do. Good questions about them are about costs and risk, not about whether speed is fair.

Lab · what's graded

  • Market participants25 pts
  • Who holds the inventory?10 pts
  • Typical HFT traits15 pts
  • Spread income20 pts
  • A market maker's cycle15 pts
  • Adverse selection15 pts
0/ 6 answered
Tasks
1Match25 ptsNot answered

Match each participant to its typical behaviour.

Pick the partner of each item on the left.

Market maker
HFT firm
Pension fund
Retail investor
Arbitrageur
2Choice10 ptsNot answered

Who takes the risk of holding shares while providing liquidity to others?

3Choice15 ptsNot answered

Select every statement that describes typical high-frequency trading.

4Numeric answer20 ptsNot answered

A market maker quotes 20.00 bid and 20.02 ask. During the day it buys 10,000 shares at the bid and sells 10,000 shares at the ask. What is the gross spread income?

income=\text{income} =income=accepted: ± 0.5
5Order the steps15 ptsNot answered

Put the steps of a market maker's cycle in order.

Drag to reorder, or focus an item, press Space to lift it, the arrow keys to move it and Space to drop it.

  1. 1Shift the quotes to encourage the opposite trade
  2. 2Quote a bid and an ask
  3. 3The opposite side fills and the spread is earned
  4. 4One side is filled and the maker now holds inventory
6Explain in words15 ptsNot answered

In two or three sentences, explain adverse selection for a market maker and how a market maker responds to it.

Math modeKeyboard or LaTeX inputTask 1 of 6 · Ctrl ⏎ to check

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