Compute negative-price probability after n steps
Company: Optiver
Role: Software Engineer
Category: Statistics & Math
Difficulty: medium
Interview Round: Take-home Project
A price starts at value s. Each day for n independent days, it moves to s + x with probability p and to s − x with probability 1 − p (x >
0). After n days, what is the probability that the final price is strictly below 0? Derive a closed-form expression (in terms of a binomial tail or equivalent) and describe an algorithm to compute it accurately for large n.
Quick Answer: This question evaluates understanding of discrete probability distributions and random-walk processes within Statistics & Math, testing skills in binomial modeling and numeric computation for probabilistic outcomes.