Citadel·Data Scientist·Technical Phone Screen
Jun 2026
Citadel data science interview that went deep into stochastic processes and trading strategy math. Four-part problem covering random walks, profit distributions, and Brownian motion limits. Felt like a quant interview wearing a data science costume.
- For a simple symmetric random walk, consider a strategy where you open a long or short position at each step based on the direction of that step, hold all positions until the final time T, and liquidate at the terminal price. Derive the expected total profit and its variance.
- Now modify the strategy so that each position is closed after just one step instead of held until the end. What are the expectation and variance of a single one-step profit, and what happens to the cumulative profit after T steps?
- Generalize the original hold-to-end strategy to a biased random walk where the probability of an up step is p, not necessarily one-half. How do the expected profit and variance change?
- Replace the discrete random walk with standard Brownian motion sampled at equally spaced intervals. Apply the same trading rule using the sampled increments, then discuss what happens to the expected profit and variance as the sampling interval shrinks to zero. Are there additional assumptions needed, and does the limit exist?
“The expectation part wasn't bad once I wrote out what each position contributes: a long at time t earns S_T minus S_t, a short earns the negative.” The rest of the author's notes on Data Scientist interview at Citadel, Technical Phone Screen round, covers how they worked through the question, what the panel pushed back on, and what they would do differently.
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