Citadel Interview Questions

If you have a dataset with many features, what methods can you use to reduce its dimensionality?

How do you derive the Black-Scholes formula for pricing European options?

1. Describe your past research experience related to reinforcement learning and model explainability. 2. Explain the bias-variance trade-off in random forests. 3. What is the closed-form solution to linear regression, with and without L2 regularization?

Analyze the variance of a momentum trading strategy.

Sample points randomly from a unit sphere. If you generate independent standard normal variables X1, X2, X3 for the three coordinates and normalize by dividing by sqrt(X1^2 + X2^2 + X3^2), then (X1, X2, X3) / sqrt(X1^2 + X2^2 + X3^2) is a uniform random point on the sphere. What is the variance of each coordinate of the resulting uniform distribution on the sphere?

Given the numbers 1 to 1000 arranged around a circle in order, start at 1 and delete every alternate number (i.e., remove 1, then 3, then 5, and so on). Continue this process of deleting every other remaining number, wrapping around the circle as necessary, until only one number remains. Determine this final remaining number.

Two people plan to meet at a train station. Each arrives at a random time between 4:00 pm and 5:00 pm and will wait 10 minutes for the other. What is the probability that they will meet?

What is implied volatility? What is the probability distribution of X + Y, where X and Y are independent and identically distributed uniform random variables?

Given a list of stock prices for consecutive days, determine the optimal strategy to maximize profit from buying and selling stocks. You may complete as many transactions as you like (i.e., buy and sell multiple times), but you must sell the stock before you buy again.