Quant interview preparation

Questions

100

Traced to a firm

53

Firms

15

Updated

September 2026

Asked at

All firmsOld Mission Capital12Tower Research Capital10Jump Trading7Akuna Capital5Citadel4DED.E. Shaw3Jane Street3ACAQR Capital Management2DRW2Millennium Management2Schonfeld2SCSquarepoint Capital2Susquehanna International Group2Belvedere Trading1Optiver1

Topic

All topicsProbability10Coins, cards and games6Expected value8Statistics11Market making15Estimation and mental maths4Stochastic processes4Regression5Machine learning6Time series6Programming10Options and derivatives8Fit and motivation7

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Type

AnyBrainteaserTechnicalCaseMarket viewFit

1. 048Asset volatility comes in clusters. What does that break, and how do you model it?Time seriesIntermediatetechnicalQuant researchRisk

   Say this

   It breaks the constant-variance assumption behind almost everything: OLS standard errors, iid return models and Black-Scholes. The standard answer is a GARCH model, where today's variance depends on yesterday's variance and yesterday's squared shock.

   Then walk it

   1. The empirical fact first: returns are close to unpredictable in the mean but their squares and absolute values are strongly autocorrelated, with the autocorrelation of squared returns decaying over weeks. Big moves cluster.
   2. GARCH(1,1) is sigma squared at t equals omega plus alpha times the last squared return plus beta times the last variance. On daily equities alpha is typically around 0.05 to 0.1 and beta around 0.85 to 0.92, with alpha plus beta just under one, meaning very persistent but eventually mean reverting.
   3. Long-run variance is omega over (1 minus alpha minus beta). If alpha plus beta hits one you get integrated GARCH, which is essentially an exponentially weighted moving average with no mean reversion, and that is what RiskMetrics used.
   4. It matters for options because it generates both fat unconditional tails and a term structure of volatility, which is why implied vol curves upward or downward towards the long-run level depending on where spot vol sits.
   5. Variants worth naming and the honest limitation: GJR-GARCH or EGARCH add the leverage effect, since negative returns raise vol more than positive ones, which plain GARCH cannot capture. And for anything intraday I would prefer realised volatility from high-frequency data, because a HAR model on realised vol usually forecasts better than GARCH on daily closes.

   Where candidates lose it

   Describing GARCH mechanically without saying what it is for. The point is that conditional variance is forecastable even when the mean is not, which is why volatility trading exists and directional trading is hard. Also do not forget the leverage effect, since plain GARCH is symmetric in the sign of returns and equity vol is not.

   Expect next

   • Why does alpha plus beta sit so close to one?
   • What is the leverage effect and which model captures it?
   • Would you use GARCH or realised volatility to forecast tomorrow's vol?
2. 057What does stationarity mean, how do you test for it, and why do you care?Time seriesIntermediatetechnicalQuant researchRisk

   Say this

   Weak stationarity means constant mean, constant variance and an autocovariance that depends only on the lag. You care because the standard inference machinery assumes it, and regressing non-stationary series on each other produces spurious relationships with impressive t statistics.

   Then walk it

   1. Prices are not stationary, they are close to a random walk with a unit root. Returns are much closer to stationary, which is why every model works on returns and not on levels.
   2. Tests: augmented Dickey-Fuller and Phillips-Perron test the null of a unit root, KPSS tests the null of stationarity. Run both, because they have opposite nulls and agreeing tests are more convincing than either alone. And these tests have low power, so failing to reject is weak evidence.
   3. Spurious regression is the cost of getting it wrong. Regress one independent random walk on another and you reject the null of no relationship far more often than five percent of the time, with an R squared that looks respectable. Granger and Newbold showed this in 1974 and people still do it.
   4. The exception that matters for trading: cointegration. Two non-stationary series can have a stationary linear combination, which is precisely the statistical statement of a pair trade. Test it with Engle-Granger or Johansen, and then the correct specification is an error-correction model rather than a regression in levels.
   5. The practical honesty: financial series are not stationary even in returns, because volatility and correlation regimes shift. So I treat stationarity as a working approximation over a limited window, and I check parameter stability across subsamples rather than trusting one test on the full history.

   Where candidates lose it

   Answering just difference it until the test passes. Over-differencing destroys the signal, and a cointegrated pair loses its whole tradeable relationship if you difference both series. Say what stationarity buys you, name the spurious regression result, and bring up cointegration unprompted since it is where the money is.

   Expect next

   • What is cointegration and how does it differ from correlation?
   • How do you test it, and what is an error-correction model?
   • What if a series is stationary in one decade and not the next?

Firm tags come from public, anonymous candidate reports on Wall Street Oasis: strong signal, not sworn testimony. Firms are named as the places a question was reported, not as partners of Fin Maverick. Answers are written for this page to show how to think out loud; they are not scripts to recite.