If you’re interviewing for a quant role in an investment bank, success won’t simply be a question of laying out your PhD and letting your thesis speak for itself. You will need to talk. You will need to answer questions. These are some the questions you should expect.
1) Can you tell me, briefly (and in words that a layman or non-quantitatively trained trader would understand) the contents of your thesis?
2) What are the limitations of Black-Scholes, implied volatility, and jump diffiusion models?
3) Are exchange rates mean reverting?
4) What test would you apply for mean reversion?
5) Why is there an n-1 term in standard deviation?
6) How do you manage risk and return using the Kelly criterion?
7) What is Itô’s Lemma?
8) What assumptions must be made regarding the properties of derivatives for Itô’s Lemma to be applied correctly?
9) Tell me a little about the big issues in your markets at the moment…
Especially for algo traders:
10) Can you explain the basic theory behind the Kalman Filter? (Expect this in algorithmic trading interviews)
11) How would you use the Kalman Filter to model stock price movements? (Expect this in algorithmic trading interviews too)
Especially for programmers:
12) How would you programme the Sieve of Eratosthenes?
13) How would you code up a smart pointer?
14) How would you code an exception safe copy constructor?
These questions have been assembled with the assistance of Dominic Connor at P&D Quant Recruitment at Trevor Symons at Selby Jennings.
An example of a longer quant question:
Here we have a supplementary quant question from Quora
15) ‘You want to evaluate an existing fixed for floating interest rate swap with 16 months remaining to maturity. Fixed side pays semi-annually, floating side pays quarterly and both sides pay at the maturity date. How many floating rate payments are left? How long until the next floating rate payment?’
US

Nice. More of this please.
You need a PhD to answer these correctly???? Certainly not if you have a MSc from a good English University!!!
These questions are mostly industry specific questions which a PhD in math, physics, EE, CS may not have seen. The true test is raw intelligence, the ability to learn fast and independently and lastly but not leastly, the ability to apply theory to practice. These questions are a red herring, as one might expect.
So why not get a MSc grad in (Mathematical) Economics, econometrics, financial mathematics – who can not only answer these questions but focus their work on quants related to the field and not come up with algoritms that work in physics or engineering or maths but are insufficient to handle human action and responses as financial and economic agents, istead of some guy who knows everyting about a particular matchbox in a matchbox factory?
I think the last poster just answered his or her own question by construction.