{
  "calculator": "quant-interview-question-generator",
  "title": "Quant Interview Question Generator",
  "site": "AI Fin Hub",
  "input": {
    "difficulty": "medium",
    "n": 8,
    "seed": 7
  },
  "defaults_used": {},
  "result": {
    "questions": [
      {
        "id": "d-m-001",
        "topic": "derivatives",
        "difficulty": "medium",
        "prompt": "Why is the Black-Scholes price of an at-the-money call approximately 0.4 · S · σ · √T?",
        "solution": "With K = S and r = q = 0: C = S·[Φ(d1) − Φ(d2)], d1 = σ√T/2, d2 = −σ√T/2. For small σ√T, Φ(d1) − Φ(d2) ≈ φ(0)·σ√T = σ√T/√(2π), so C ≈ 0.3989·S·σ√T ≈ 0.4·S·σ√T."
      },
      {
        "id": "s-m-001",
        "topic": "stats",
        "difficulty": "medium",
        "prompt": "You estimate Sharpe = 1.0 over 252 days. Construct an approximate 95% CI on the annualized Sharpe.",
        "solution": "Lo (2002), i.i.d. returns: SE(SR) ≈ √((1 + SR²/2) / n) with SR and n in the SAME period. Daily: SR_d = 1/√252 ≈ 0.063, n = 252 → SE_d ≈ √(1.002/252) ≈ 0.063. Annualize ×√252 → SE ≈ 1.0, so the 95% CI is roughly 1 ± 2, i.e. about −1 to 3. Equivalently SE(SR_ann) ≈ √((1 + SR_ann²/(2·252)) / years). One year of data cannot distinguish a Sharpe-1 strategy from zero; plugging the annual SR into the daily n (√(1.5/252) ≈ 0.08) is the classic mistake."
      },
      {
        "id": "m-m-001",
        "topic": "microstructure",
        "difficulty": "medium",
        "prompt": "What is adverse selection in an order book?",
        "solution": "Resting limit orders get hit when price moves against them — informed traders pick off stale quotes. Market makers price this into the spread."
      },
      {
        "id": "p-m-002",
        "topic": "probability",
        "difficulty": "medium",
        "prompt": "100 people board a plane in order; the first sits randomly, others in their assigned seat if free, else random. P(last person gets their assigned seat)?",
        "solution": "Classic — 1/2. Symmetry: only seat 1 vs seat 100 ever matter, equally likely to be taken first."
      },
      {
        "id": "p-m-003",
        "topic": "probability",
        "difficulty": "medium",
        "prompt": "X and Y are i.i.d. uniform on [0,1]. What is P(|X − Y| < 0.1)?",
        "solution": "Geometric: area of |X−Y|<0.1 strip in unit square = 1 − (0.9)^2 = 0.19."
      },
      {
        "id": "s-m-002",
        "topic": "stats",
        "difficulty": "medium",
        "prompt": "Why does multiple-testing inflate the false-discovery rate, and what's one classic correction?",
        "solution": "Each test has α false-positive rate; K independent tests → expected K·α false positives. Bonferroni: divide α by K. BH (Benjamini-Hochberg): controls expected FDR at q."
      },
      {
        "id": "s-m-003",
        "topic": "stats",
        "difficulty": "medium",
        "prompt": "What is the bias-variance decomposition of MSE?",
        "solution": "MSE(θ̂) = Bias(θ̂)² + Var(θ̂). Total error trades off systematic miss against estimator volatility."
      },
      {
        "id": "r-m-002",
        "topic": "regression",
        "difficulty": "medium",
        "prompt": "Why are robust (HAC / Newey-West) standard errors used in financial regressions?",
        "solution": "Returns and residuals are heteroskedastic and serially correlated. Vanilla OLS SEs assume i.i.d. residuals → understate uncertainty. Newey-West corrects for autocorrelation up to chosen lag."
      }
    ],
    "totalInBank": 45
  },
  "provenance": {
    "run": "https://aifinhub.io/api/run/quant-interview-question-generator?difficulty=medium&n=8&seed=7",
    "page": "https://aifinhub.io/quant-interview-question-generator/",
    "methodology": "https://aifinhub.io/methodology/quant-interview-question-generator/",
    "contract": "https://aifinhub.io/contracts/quant-interview-question-generator.json",
    "engine": "https://aifinhub.io/engines/quant-interview-question-generator.js",
    "engine_sha256": "ca4226d7633b4bb49aecbcb41e38367d737f0662648c9b7713ebd59b4dc12b51",
    "build": "9e8a56a16bda662ba90601b49561a2b176e9c379"
  },
  "disclaimer": "Planning estimates only — not financial, tax, or investment advice.",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "cite": "AI Fin Hub, Quant Interview Question Generator (engine ca4226d7633b), https://aifinhub.io/api/run/quant-interview-question-generator?difficulty=medium&n=8&seed=7"
}