Medium · Stochastic Calculus · Multiple choice · ~5 min · #70

Which Powers of W Are Martingales?

Real interview · Morgan Stanley

Let $W_t$ be a standard Brownian motion. For which non-negative integers $n$ is $W_t^n$ a martingale? Select all that apply.

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Worked solution

Give the problem an honest attempt first, then reveal the full explanation.

Reported in interviews

Morgan Stanley· Quantitative Finance Summer AssociateGlassdoor interview question

Candidate-reported and unverified; the firm may phrase it differently or no longer ask it. The wording here is our own paraphrase, and the solution was written and checked independently of any answers posted at the source.

Concepts

Itô's lemmaDrift of a martingale

Relevant for

Quant ResearcherDesk Quant