Tudor·Data Scientist·Technical Phone Screen
Jul 2026
Tudor data science interview, heavy on statistics and stochastic processes. Two problems back to back, both around volatility estimation. The second one was genuinely hard and I don't think I fully nailed the MSE comparison.
- You have 100 independent draws from a normal distribution with known mean zero and unknown standard deviation. Propose an estimator for the standard deviation, check whether it's unbiased, and if not, explain how to correct it.
- A scaled Brownian motion is observed at 100 integer time points. You define the running max H, the running min L, the terminal value C, and the range R = H minus L. How would you compare calibrated versions of |C|, R minus |C|/2, and R squared plus C squared as estimators of volatility, and which do you prefer under a mean-squared-error criterion?
“This is the warm-up question and I knew it, but I still fumbled the bias correction explanation a bit.”