Round 1: Investment Bank Quantitative Research
Question: An ant is placed on one vertex of a unit cube. What is the shortest path the ant can take to get to the opposite vertex (walking on the surface of the cube, it cannot fly)?
Round 1: Investment Bank Quantitative Research
Question: An ant is placed on one vertex of a unit cube. What is the shortest path the ant can take to get to the opposite vertex (walking on the surface of the cube, it cannot fly)?
Round 2: Investment Bank Quantitative Research
Question 1: In Monte Carlo simulation, name a few ways to reduce variance.
Question 2: Give an example (in finance) where you would use control variates?
Round 1: Investment Bank Quantitative Research
Question: Calculate the first derivative of evaluated at using points to accuracy
Round 1: Investment Bank Quantitative Research
Question 1: Name the three (3) properties of a standard Brownian Motion.
Question 2: Let be a Brownian Motion. Is a martingale? What about ?
Round 1: Hedge Fund Quantitative Research
Question 1: If you have data of two variables, how do you check whether they are linearly correlated or not?
Question 2: Can you quantify the correlation?
Round 2: Investment Bank Quantitative Research
Question 1: What is the variance of a Brownian Motion at time ?
Question 2: What is , where is a Brownian Motion at time ?
Question 3: Given that , what is the probability that for ? That is, find
Round 1: Investment Bank Quantitative Research
Question 1: Define a Martingale.
Question 2: Give examples of Martingales (in the context of finance, preferably).
Round 1: Investment Bank Quantitative Research
Question 1: Give an example of a Ito Diffusion Equation (Stochastic Differential Equation).
Question 2: Apply Ito’s Lemma to Geometric Brownian Motion in the general case. That is, for , given , what is ?
Round 1: Investment Bank Quantitative Research
Question: Evaluate