150 Most Frequently Asked Questions On Quant Interviews (2025)

| # | Question | Difficulty | Key Idea | |---|----------|------------|-----------| | 101 | What is a martingale? | ★★★ | E[X_n+1 | F_n] = X_n | | 102 | What is Brownian motion? | ★★ | Continuous, Gaussian increments, independent | | 103 | What is a Poisson process? | ★★ | Exponential interarrival times | | 104 | What is a random walk? | ★ | S_n = X_1 + … + X_n | | 105 | What is the difference between AR(1) and MA(1)? | ★★ | AR uses past values, MA uses past errors | | 106 | What is stationarity? | ★ | Mean and variance constant over time | | 107 | What is a unit root? | ★★★ | Non-stationary, e.g., random walk | | 108 | What is the autocorrelation function? | ★ | Correlation with lagged self | | 109 | What is the Wiener process? | ★★ | Another name for Brownian motion | | 110 | What is Itô’s lemma? | ★★★ | Stochastic chain rule | | 111 | What is a stopping time? | ★★ | Decision rule based on info up to now | | 112 | What is the reflection principle for Brownian motion? | ★★★ | P(sup > a) = 2P(B_t > a) | | 113 | What is the Markov property? | ★ | Future independent of past given present | | 114 | What is a Kalman filter? | ★★★ | Recursive Bayesian estimation | | 115 | What is GARCH? | ★★★ | Volatility clustering model |

Now face-to-face with Elena, a poker-faced quant researcher.

Elena: "You flip a fair coin until you see 'Heads, Tails, Heads.' What’s the expected number of flips?"

Alex knows this is a Markov chain classic. He draws states: ∅, H, HT. Let E = expected from start. E = 1 + 0.5E(H) + 0.5E. Then E(H) = 1 + 0.5E(HT) + 0.5E(H). E(HT) = 1 + 0.5*E (since after HT, if T→reset, if H→HTH, game ends). Solving gives E = 10.

Elena: "Fine. Now, I randomly pick a number from a normal distribution N(0,1) and tell you it’s positive. What’s the expected value given that?" 150 Most Frequently Asked Questions On Quant Interviews

Alex: "That’s the mean of a truncated normal. E[X | X>0] = √(2/π) ≈ 0.798."

Elena: "Why not 0.5?"

Alex: "Because the normal is symmetric but we cut off half the distribution – the expected value shifts to the conditional mean, not the median."

She nods. "Let’s move to coding."

Final round with the head of the desk, Priya.

Priya: "You’re market making a stock at bid $10.00, ask $10.05. A buy market order comes in. You sell at $10.05. How do you hedge?"

Alex: "I’d short the stock at $10.05 to delta-neutral, then adjust based on my inventory. If I have positive gamma from options, I’d hedge dynamically."

Priya: "The stock then drops to $9.95. You lose $0.10 on the stock hedge but made $0.05 on the spread. Net –$0.05. Why not just avoid the trade?" | # | Question | Difficulty | Key

Alex: "Because over many trades, the spread is positive expectancy. The loss is inventory risk, which I can hedge further with options or futures."

Priya: "So why you? Why not a pure math major?"

Alex leans in. "Because physics taught me to model uncertainty with differential equations – but finance taught me that the real skill is knowing when your model is wrong. The 150 questions get you in the door. Not panicking when the model breaks gets you the job."

Priya extends her hand. "We’ll call you." Now face-to-face with Elena, a poker-faced quant researcher